CONSTRUCTION AND DECODING OF BCH CODES OVER CHAIN OF COMMUTATIVE RINGS

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SHAH TARIQ; QAMAR ATTIQ; DE ANDRADE ANTONIO APARECIDO

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Journal: MATHEMATICAL SCIENCES Year:2012 | Volume:6 | Issue:- Page(s): 1-14

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Title

CONSTRUCTION AND DECODING OF BCH CODES OVER CHAIN OF COMMUTATIVE RINGS

Author(s)

SHAH TARIQ | QAMAR ATTIQ | DE ANDRADE ANTONIO APARECIDO | Issue Writer Certificate

Keywords

UNITS OF A GALOIS RING

BCH CODE

MCCOY RANK

DIRECT PRODUCT OF GALOIS RINGS

Abstract

In this paper, we present a new construction and decoding of BCH CODEs over certain rings. Thus, for a nonnegative integer t, let A0⊂A1⊂…⊂At−1⊂At be a chain of unitary commutative rings, where each Ai is constructed by the direct product of appropriate Galois rings, and its projection to the fields is K0⊂K1⊂…⊂Kt−1⊂Kt (another chain of unitary commutative rings), where each Ki is made by the direct product of corresponding residue fields of given Galois rings. Also, A∗i and K∗i are the groups of units of Ai and Ki, respectively. This correspondence presents a construction technique of generator polynomials of the sequence of Bose, Chaudhuri, and Hocquenghem (BCH) codes possessing entries from A∗i and K∗i for each i, where 0≤i≤t. By the construction of BCH CODEs, we are confined to get the best code rate and error correction capability; however, the proposed contribution offers a choice to opt a worthy BCH CODE concerning code rate and error correction capability. In the second phase, we extend the modified Berlekamp-Massey algorithm for the above chains of unitary commutative local rings in such a way that the error will be corrected of the sequences of codewords from the sequences of BCH CODEs at once. This process is not much different than the original one, but it deals a sequence of codewords from the sequence of codes over the chain of Galois rings.

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APA: Copy

SHAH, TARIQ, QAMAR, ATTIQ, & DE ANDRADE, ANTONIO APARECIDO. (2012). CONSTRUCTION AND DECODING OF BCH CODES OVER CHAIN OF COMMUTATIVE RINGS. MATHEMATICAL SCIENCES, 6(-), 1-14. SID. https://sid.ir/paper/322624/en

Vancouver: Copy

SHAH TARIQ, QAMAR ATTIQ, DE ANDRADE ANTONIO APARECIDO. CONSTRUCTION AND DECODING OF BCH CODES OVER CHAIN OF COMMUTATIVE RINGS. MATHEMATICAL SCIENCES[Internet]. 2012;6(-):1-14. Available from: https://sid.ir/paper/322624/en

IEEE: Copy

TARIQ SHAH, ATTIQ QAMAR, and ANTONIO APARECIDO DE ANDRADE, “CONSTRUCTION AND DECODING OF BCH CODES OVER CHAIN OF COMMUTATIVE RINGS,” MATHEMATICAL SCIENCES, vol. 6, no. -, pp. 1–14, 2012, [Online]. Available: https://sid.ir/paper/322624/en

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