Z2Z4-additive cyclic codes, generator polynomials and dual codes

2014/06/17 by Joaquim Borges, Borges, Joaquim, Cristina Fernández-Córdoba +3 · 1 citation
Computer Science · Engineering · Mathematics · #68Rxx #Coding theory and cryptography #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Finite Group Theory Research #Information Theory (cs.IT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1406.4425

openalex publication_date 2014/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A ℤ₂ℤ₄-additive code \cal C⊆ℤ₂^α×ℤ₄^β is called cyclic if the set of coordinates can be partitioned into two subsets, the set of ℤ₂ and the set of ℤ₄ coordinates, such that any cyclic shift of the coordinates of both subsets leaves the code invariant. These codes can be identified as submodules of the ℤ₄[x]-module ℤ₂[x]/(x^α-1)×ℤ₄[x]/(x^β-1). The parameters of a ℤ₂ℤ₄-additive cyclic code are stated in terms of the degrees of the generator polynomials of the code. The generator polynomials of the dual code of a ℤ₂ℤ₄-additive cyclic code are determined in terms of the generator polynomials of the code \cal C.

Cited by

• A characterization of ℤ₂ℤ₂[u]-linear codes

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