Codes over infinite family of rings : Equivalence and invariant ring

Irwansyah,; Muchtadi-Alamsyah, Intan; Muchlis, Ahmad; Barra, Aleams; Suprijanto, Djoko

doi:10.1063/1.4940810

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Theorem 221

Cyclic and Quasi-cyclic Codes Over B K1

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2017

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“…Proof. From the facts that Φ k is a distance preserving map and the Hamming weight enumerator for codes over B k satisfies the MacWilliams relation as in [16] (see Section 3.3), we have the Hamming weight enumerator for Φ k (C) also satisfies the MacWilliams relation.…”

Section: Theorem 22mentioning

confidence: 97%

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Structure of linear codes over the ring $B_k$

Irwansyah

Suprijanto

2017

Preprint

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We study the structure of linear codes over the ring B k which is defined by. In order to study the codes, we begin with studying the structure of the ring B k via a Gray map which also induces a relation between codes over B k and codes over F p r . We consider Euclidean and Hermitian self-dual codes, MacWilliams relations, as well as Singleton-type bounds for these codes. Further, we characterize cyclic and quasi-cyclic codes using their images under the Gray map, and give the generators for these type of codes.

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Section: Theorem 22mentioning

confidence: 97%

“…In this section we will characterize quasi-cyclic and cyclic codes over B k in terms of their images under the Gray map ϕ. We refer to [16] to see how the Gray map works.…”

Section: Cyclic and Quasi-cyclic Codes Over B Kmentioning

confidence: 99%