An explicit representation and enumeration for negacyclic codes of length 2^kn over ℤ₄+uℤ₄

2018/11/27 by Yonglin Cao, Cao, Yonglin, Yuan Cao +5
Computer Science · Engineering · #Coding theory and cryptography #Cryptographic Implementations and Security #FOS: Computer and information sciences #Information Theory (cs.IT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1811.10991

openalex publication_date 2018/11/27 · openalex created_date 2018/12/11 · openalex updated_date 2026/07/28

Abstract

In this paper, an explicit representation and enumeration for negacyclic codes of length 2^kn over the local non-principal ideal ring R=ℤ₄+uℤ₄ (u²=0) is provided, where k, n are any positive integers and n is odd. As a corollary, all distinct negacyclic codes of length 2^k over R are listed precisely. Moreover, a mass formula for the number of negacyclic codes of length 2^kn over R is given and a mistake in [Cryptogr. Commun. (2017) 9: 241--272] is corrected.

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