Second Supplemental Indenture, dated November 17, 2017, by and between Brocade Communications Systems, Inc. and Wells Fargo Bank, National Association

Exhibit 4.1

BROCADE COMMUNICATIONS SYSTEMS, INC.

AND

WELLS FARGO BANK, NATIONAL ASSOCIATION,

as Trustee

SECOND SUPPLEMENTAL INDENTURE

Dated as of November 17, 2017

1.375% Convertible Senior Notes due 2020

SECOND SUPPLEMENTAL INDENTURE, dated as of November 17, 2017 (this “Supplemental Indenture”), among Brocade Communications Systems, Inc., a Delaware corporation (the “Company”), as issuer, and Wells Fargo Bank, National Association, a national banking association organized under the laws of the United States of America, as trustee (the “Trustee”), to the Indenture, dated as of January 14, 2015 (as supplemented or otherwise modified prior to the date hereof, the “Indenture”), between the Company and the Trustee.

WHEREAS, the Company has heretofore executed and delivered the Indenture, pursuant to which the Company issued its 1.375% Convertible Senior Notes due 2020 (the “Notes”) in the original aggregate principal amount of $575,000,000, convertible under certain circumstances into cash and/or shares of the Company’s common stock, par value $0.001 per share (“Company Common Stock”), at the Company’s option;

WHEREAS, the Company has entered into an Agreement and Plan of Merger, dated as of November 2, 2016 (as amended, supplemented, restated or otherwise modified, the “Merger Agreement”), by and among the Company, Broadcom Limited, a limited company organized under the laws of the Republic of Singapore (“Ultimate Parent”), Broadcom Corporation, a California corporation and indirect subsidiary of Ultimate Parent (“Parent”), and Bobcat Merger Sub, Inc., a Delaware corporation and direct wholly owned subsidiary of Parent (“Merger Sub”);

WHEREAS, on December 19, 2016, Parent assigned all of its rights under the Merger Agreement and transferred all of the issued and outstanding capital stock of Merger Sub to LSI Corporation, a Delaware corporation and an indirect subsidiary of Ultimate Parent (“LSI”);

WHEREAS, pursuant to the terms of the Merger Agreement, Merger Sub will merge with and into the Company (the “Merger”) with the Company, as the surviving entity in the Merger, becoming a wholly owned subsidiary of LSI as of the date hereof;

WHEREAS, the Merger constitutes a Merger Event under the Indenture and Section 14.07(a) of the Indenture provides that in the case of any Merger Event, prior to or at the effective time of such Merger Event, the Company shall execute and deliver to the Trustee a supplemental indenture permitted under Section 10.01(i) of the Indenture providing that the right to convert each $1,000 principal amount of Notes shall be changed into a right to convert such principal amount of Notes into Reference Property upon such Merger Event;

WHEREAS, in connection with the Merger, each outstanding share of Company Common Stock will be converted into the right to receive an amount in cash equal to $12.75 in accordance with the terms of the Merger Agreement;

WHEREAS, pursuant to Section 10.01 of the Indenture, the Company and the Trustee may enter into indentures supplemental to the Indenture to, among other things, (i) make any change that does not adversely affect the rights of any Holder or (ii) in connection with any Merger Event, provide that the Notes are convertible into Reference Property, subject to the provisions of Section 14.02, and make such related changes to the terms of the Notes in accordance with Section 14.07;

WHEREAS, the Board of Directors of the Company by resolutions adopted on June 6, 2017 and the Audit Committee of the Board of Directors of the Company by resolutions adopted on November 6, 2017, have duly authorized this Supplemental Indenture, and the entry into this Supplemental Indenture by the parties hereto is permitted by the provisions of the Indenture;

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WHEREAS, in connection with the execution and delivery of this Supplemental Indenture, the Trustee has received an Officer’s Certificate and an Opinion of Counsel as contemplated by Section 17.05 of the Indenture; and

WHEREAS, the Company has requested that the Trustee execute and deliver this Supplemental Indenture and have satisfied all requirements necessary to make this Supplemental Indenture a valid instrument in accordance with its terms.

WITNESSETH:

NOW THEREFORE, each party agrees as follows for the benefit of the other parties and for the equal and ratable benefit of the Holders:

ARTICLE 1

DEFINITIONS

Section 1.01. Definitions in the Supplemental Indenture. Unless otherwise specified herein or the context otherwise requires:

(a) a term defined in the Indenture has the same meaning when used in this Supplemental Indenture unless the definition of such term is amended or supplemented pursuant to this Supplemental Indenture;

(b) the terms defined in this Article and in this Supplemental Indenture include the plural as well as the singular;

(c) unless otherwise stated, a reference to a Section or Article is to a Section or Article of this Supplemental Indenture; and

(d) Article and Section headings herein are for convenience only and shall not affect the construction hereof.

Section 1.02. Reference Property. In accordance with Section 14.07(a) of the Indenture and pursuant to the terms of the Merger Agreement, a “unit of Reference Property” shall mean $12.75 in cash.

Section 1.03. Initial Dividend Threshold. In accordance with Section 14.07(e)(iii) of the Indenture, the Initial Dividend Threshold, at and after the effective time of the Merger, shall be zero.

ARTICLE 2

EFFECT OF MERGER ON CONVERSION

Section 2.01. Conversion Right. In accordance with and subject to Section 14.07 of the Indenture, as a result of the Merger, each $1,000 in principal amount of Notes is, at and after the effective time of the Merger, convertible in accordance with the terms of the Indenture into the right to receive the amount of cash that a holder of a number of shares of Company Common Stock equal to the Conversion Rate immediately prior to the consummation of the Merger would have owned or been entitled to receive upon the Merger. For all conversions that occur after the effective time of the Merger in accordance with and subject to Article 14 of the Indenture, (i) the consideration due upon conversion of each $1,000 principal amount of Notes shall be solely cash in an amount equal to the Conversion Rate in effect on the

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Conversion Date (as may be increased by any Additional Shares pursuant to Section 14.03 of the Indenture), multiplied by $12.75, and (ii) the Company shall satisfy the conversion obligation by paying cash to converting Holders on the third Business Day immediately following the relevant Conversion Date.

Section 2.02. Addresses for Notices, Etc. The first paragraph of Section 17.03 of the Indenture is hereby amended by deleting such paragraph in its entirety and replacing it with the following:

“Section 17.03. Addresses for Notices, Etc. Any notice or demand that by any provision of this Indenture is required or permitted to be given or served by the Trustee or by the Holders on the Company shall be deemed to have been sufficiently given or made, for all purposes if given or served by being deposited postage prepaid by registered or certified mail in a post office letter box addressed (until another address is filed by the Company with the Trustee) to the Company at the address of its principal office at 1320 Ridder Park Drive, San Jose, California 95131, Attention: Rebecca Boyden. Any notice, direction, request or demand hereunder to or upon the Trustee shall be deemed to have been sufficiently given or made, for all purposes, if given or served by being deposited postage prepaid by registered or certified mail in a post office letter box addressed to the Corporate Trust Office or sent electronically in PDF format.”

ARTICLE 3

MISCELLANEOUS

Section 3.01. Ratification of Indenture. The Indenture, as supplemented by this Supplemental Indenture, is in all respects ratified and confirmed, and this Supplemental Indenture shall be deemed part of the Indenture in the manner and to the extent herein and therein provided.

Section 3.02. Trustee Not Responsible for Recitals. The recitals herein contained are made by the Company and not by the Trustee, and the Trustee assumes no responsibility for the correctness thereof. The Trustee makes no representation as to the validity or sufficiency of this Supplemental Indenture. All of the provisions contained in the Indenture in respect of the rights, privileges, immunities, powers, and duties of the Trustee shall be applicable in respect of the Supplemental Indenture as fully and with like force and effect as though set forth in full herein.

Section 3.03 Successors. All agreements of the Company and the Trustee in this Supplemental Indenture will bind their respective successors.

Section 3.04. Governing Law. THIS SUPPLEMENTAL INDENTURE AND ANY CLAIM, CONTROVERSY OR DISPUTE ARISING UNDER OR RELATED TO THIS SUPPLEMENTAL INDENTURE SHALL BE GOVERNED BY, AND CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW YORK.

Section 3.05. Headings, Etc. The titles and headings of the articles and sections of this Supplemental Indenture have been inserted for convenience of reference only, are not to be considered a part hereof, and shall in no way modify or restrict any of the terms or provisions hereof.

Section 3.06. Execution in Counterparts. This Supplemental Indenture may be executed in any number of counterparts, each of which shall be an original, but such counterparts shall together constitute but one and the same instrument. The exchange of copies of this Supplemental Indenture and of signature

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pages by facsimile or PDF transmission shall constitute effective execution and delivery of this Supplemental Indenture as to the parties hereto and may be used in lieu of the original Supplemental Indenture for all purposes. Signatures of the parties hereto transmitted by facsimile or PDF shall be deemed to be their original signatures for all purposes.

Section 3.07. Severability. In the event any provision of this Supplemental Indenture shall be invalid, illegal or unenforceable, then (to the extent permitted by law) the validity, legality or enforceability of the remaining provisions shall not in any way be affected or impaired.

Section 3.08. Waiver of Jury Trial. EACH OF THE COMPANY AND THE TRUSTEE HEREBY IRREVOCABLY WAIVES, TO THE FULLEST EXTENT PERMITTED BY APPLICABLE LAW, ANY AND ALL RIGHT TO TRIAL BY JURY IN ANY LEGAL PROCEEDING ARISING OUT OF OR RELATING TO THIS SUPPLEMENTAL INDENTURE OR THE TRANSACTIONS CONTEMPLATED HEREBY.

Section 3.09. Effectiveness. This Supplemental Indenture shall become effective upon, without further action by the parties hereto, the Effective Time.

[Signature Page Follows]

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IN WITNESS WHEREOF, the parties hereto have caused this Supplemental Indenture to be duly executed as of the day and year first above written.

SIGNATURE PAGE TO SUPPLEMENTAL INDENTURE