An Algorithm for Computing the Minimum Distances of Extensions of BCH Codes Embedded in Semigroup Rings

Cazaran, Jilyana; Kelarev, AV; Quinn, Stephen; Vertigan, DL

doi:10.1007/s00233-006-0647-9

Cited by 24 publications

(20 citation statements)

References 38 publications

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“…However, the extension of a BCH code C embedded in a semigroup ring F [S], where S is a finite semigroup, was considered in 2006 by Cazaran et. all [4], where an algorithm was presented for computing the weights of extensions for these codes embedded in semigroup rings as ideals. A lot of information concerning various ring constructions and about polynomial codes is given by Kelarev [5].…”

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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“…The present paper uses contracted semigroup rings, which helps to record our results more concisely. These constructions are used and considered, for example, in [1,9,11,12,14,16,32].…”

Section: Preliminariesmentioning

confidence: 99%

Rees Matrix Constructions for Clustering of Data

Kelarev¹,

Watters²,

Yearwood³

2009

J. Aust. Math. Soc.

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This paper continues the investigation of semigroup constructions motivated by applications in data mining. We give a complete description of the error-correcting capabilities of a large family of clusterers based on Rees matrix semigroups well known in semigroup theory. This result strengthens and complements previous formulas recently obtained in the literature. Examples show that our theorems do not generalize to other classes of semigroups.2000 Mathematics subject classification: primary 16S36, 20M35; secondary 20M25, 68T.

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“…The extension of a BCH code embedded in a semigroup ring is considered in [7]. A great amount of information regarding rings construction and its corresponding polynomial codes is given in [8].…”

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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An Algorithm for Computing the Minimum Distances of Extensions of BCH Codes Embedded in Semigroup Rings

Abstract: An algorithm is given for computing the weights of extensions of BCH codes embedded in semigroup rings as ideals. The algorithm relies on a more general technical result of independent interest.

Cited by 24 publications

References 38 publications

Encoding through generalized polynomial codes

Encoding through generalized polynomial codes

Rees Matrix Constructions for Clustering of Data

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

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