On Linear Codes over ℤ₄+vℤ₄

2014/02/27 by Jian Gao, Yun Gao, Gao, Jian +4 · 1 citation
Computer Science · Engineering · Mathematics · #94B05 #94B15 #Cellular Automata and Applications #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #graph theory and CDMA systems #math.IT #msc:94B05 #msc:94B15

paper · pdf · doi:10.48550/arxiv.1402.6771

25 pages

openalex publication_date 2014/02/27 · arxiv created 2014/12/31 · arxiv updated 2015/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Linear codes are considered over the ring ℤ₄+vℤ₄, where v²=v. Gray weight, Gray maps for linear codes are defined and MacWilliams identity for the Gray weight enumerator is given. Self-dual codes, construction of Euclidean isodual codes, unimodular complex lattices, MDS codes and MGDS codes over ℤ₄+vℤ₄ are studied. Cyclic codes and quadratic residue codes are also considered. Finally, some examples for illustrating the main work are given.

Cited by

• Self-dual codes and quadratic residue codes over the ring ℤ₉+uℤ₉

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