Generators and weights of polynomial codes

Cazaran, Jilyana; Kelarev, AV

doi:10.1007/s000130050149

Cited by 29 publications

(20 citation statements)

References 10 publications

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“…On the above ideas, Cazaran and Kelarev [2] established necessary and sufficient conditions for an ideal to have a single generator and described all finite quotient rings Z m [X 1 , • • • , X n ]/I, where I is an ideal generated by univariate polynomials which are commutative principal ideal rings. In another paper, Cazaran and Kelarev [3] obtained conditions for the certain rings to be finite commutative principal ideal rings.…”

Section: Encoding Through Generalized Polynomial Codesmentioning

confidence: 99%

Encoding through generalized polynomial codes

Shah

Khan

Andrade³

2011

Comput. Appl. Math.

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Section: Encoding Through Generalized Polynomial Codesmentioning

confidence: 99%

Encoding through generalized polynomial codes

Shah

Khan

Andrade³

2011

Comput. Appl. Math.

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“…Though most of the conventional error-correcting codes are principal ideals in the factor ring of a polynomial ring in one indeterminate. In [5], instead of one indeterminate, the authors have given the necessary and sufficient conditions for an ideal to have a single generator while, in [6], they have described all , where J is an ideal generated by univariate polynomials.…”

Section: Introductionmentioning

confidence: 99%

An association between primitive and non-primitive BCH codes using monoid rings

Ansari

Shah

2016

J Wireless Com Network

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BCH codes are one of the most important classes of cyclic codes for error correction. In this study, we generalize BCH codes using monoid rings instead of a polynomial ring over the binary field F 2 . We show the existence of a non-primitive binary BCH code C bn of length bn, corresponding to a given length n binary BCH code C n . The value of b is investigated for which the existence of the non-primitive BCH code C bn is assured. It is noticed that the code C n is embedded in the code C bn . Therefore, encoding and decoding of the codes C n and C bn can be done simultaneously. The data transmitted by C n can also be transmitted by C bn . The BCH code C bn has better error correction capability whereas the BCH code C n has better code rate, hence both gains can be achieved at the same time.

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“…In [4] Cazaran and Kelarev introduce the necessary and sufficient conditions for the ideal to be a principal ideal and describe all finite principal ideal rings Z m [x 1 , x 2 , · · · , x n ]/I, where I is generated by univariate polynomials. Moreover, in [5], they obtained conditions for certain rings to be finite commutative principal ideal rings.…”

Section: Introductionmentioning

confidence: 99%

A BCH code and a sequence of cyclic codes

Andrade¹,

Shah²,

Khan³

2014

ija

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This study establishes that for a given binary BCH code C 0 n of length n generated by a polynomial g(x) ∈ F 2 [x] of degree r there exists a family of binary cyclic codes {C m 2 m−1 (n+1)n } m≥1 such that for each m ≥ 1, the binary cyclic code C m 2 m−1 (n+1)n has length 2 m−1 (n + 1)n and is generated by a generalized polynomial g(x2 m (n+1)n for each m ≥ 1. By a newly proposed algorithm, codewords of the binary BCH code C 0 n can be transmitted with high code rate and decoded by the decoder of any member of the family {C m 2 m−1 (n+1)n } m≥1 of binary cyclic codes, having the same code rate.Mathematics Subject Classification: 11T71, 14A50, 94A15

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Generators and weights of polynomial codes

Cited by 29 publications

References 10 publications

Encoding through generalized polynomial codes

Encoding through generalized polynomial codes

An association between primitive and non-primitive BCH codes using monoid rings

A BCH code and a sequence of cyclic codes

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