A cyclic [6,3,4] group code and the hexacode over GF(4)

Moshe Ran; Jakov Snyders

doi:10.1109/18.508851

A cyclic [6,3,4] group code and the hexacode over GF(4)

Moshe Ran^*, Jakov Snyders

^*Corresponding author for this work

Department of Electrical Engineering - Systems

Research output: Contribution to journal › Article › peer-review

Abstract

A [6,3,4] code E₆ over an Abelian group A₄ with four elements is presented. E₆ is cyclic, unlike the [6,3,4] hexacode H₆ over GF(4) However, E₆ and H₆, are isomorphic when the latter is viewed as a group code. Differences and similarities between E₆ and H₆ are discussed. A dual code of E₆ is presented. Some binary codes, among them the [24,12,8]Golay, are derived with the aid of E₆. A related cyclic [4,2,3] code E*₄ is applied to construct the Nordstrom-Rohinson code. E₆ is the smallest member of a class of [2k, k, 4] cyclic and reversible codes over A₄. Another class of cyclic and reversible codes of length 2ℓ + 1 ; ℓ ≥ 2 and minimum distance 3 over A₄ is also presented.

Original language	English
Pages (from-to)	1250-1253
Number of pages	4
Journal	IEEE Transactions on Information Theory
Volume	42
Issue number	4
DOIs	https://doi.org/10.1109/18.508851
State	Published - 1996

Keywords

Binary image
Cyclic code
Elementary Abelian group
Group code
Hcxacode

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title = "A cyclic [6,3,4] group code and the hexacode over GF(4)",

abstract = "A [6,3,4] code E6 over an Abelian group A4 with four elements is presented. E6 is cyclic, unlike the [6,3,4] hexacode H6 over GF(4) However, E6 and H6, are isomorphic when the latter is viewed as a group code. Differences and similarities between E6 and H6 are discussed. A dual code of E6 is presented. Some binary codes, among them the [24,12,8]Golay, are derived with the aid of E6. A related cyclic [4,2,3] code E*4 is applied to construct the Nordstrom-Rohinson code. E6 is the smallest member of a class of [2k, k, 4] cyclic and reversible codes over A4. Another class of cyclic and reversible codes of length 2ℓ + 1 ; ℓ ≥ 2 and minimum distance 3 over A4 is also presented.",

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author = "Moshe Ran and Jakov Snyders",

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AU - Snyders, Jakov

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N2 - A [6,3,4] code E6 over an Abelian group A4 with four elements is presented. E6 is cyclic, unlike the [6,3,4] hexacode H6 over GF(4) However, E6 and H6, are isomorphic when the latter is viewed as a group code. Differences and similarities between E6 and H6 are discussed. A dual code of E6 is presented. Some binary codes, among them the [24,12,8]Golay, are derived with the aid of E6. A related cyclic [4,2,3] code E*4 is applied to construct the Nordstrom-Rohinson code. E6 is the smallest member of a class of [2k, k, 4] cyclic and reversible codes over A4. Another class of cyclic and reversible codes of length 2ℓ + 1 ; ℓ ≥ 2 and minimum distance 3 over A4 is also presented.

AB - A [6,3,4] code E6 over an Abelian group A4 with four elements is presented. E6 is cyclic, unlike the [6,3,4] hexacode H6 over GF(4) However, E6 and H6, are isomorphic when the latter is viewed as a group code. Differences and similarities between E6 and H6 are discussed. A dual code of E6 is presented. Some binary codes, among them the [24,12,8]Golay, are derived with the aid of E6. A related cyclic [4,2,3] code E*4 is applied to construct the Nordstrom-Rohinson code. E6 is the smallest member of a class of [2k, k, 4] cyclic and reversible codes over A4. Another class of cyclic and reversible codes of length 2ℓ + 1 ; ℓ ≥ 2 and minimum distance 3 over A4 is also presented.

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A cyclic [6,3,4] group code and the hexacode over GF(4)

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Keywords

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