Note on the residue codes of self-dual ℤ₄-codes having large minimum Lee weights

2014/01/24 by Masaaki Harada, Harada, Masaaki
Computer Science · Mathematics · #94B05 #Coding theory and cryptography #Combinatorics (math.CO) #Cooperative Communication and Network Coding #FOS: Computer and information sciences #FOS: Mathematics #Finite Group Theory Research #Information Theory (cs.IT)

paper · pdf · doi:10.48550/arxiv.1401.6252

openalex publication_date 2014/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is shown that the residue code of a self-dual ℤ₄-code of length 24k (resp. 24k+8) and minimum Lee weight 8k+4 or 8k+2 (resp. 8k+8 or 8k+6) is a binary extremal doubly even self-dual code for every positive integer k. A number of new self-dual ℤ₄-codes of length 24 and minimum Lee weight 10 are constructed using the above characterization. These codes are Type I ℤ₄-codes having the largest minimum Lee weight and the largest Euclidean weight among all Type I ℤ₄-codes of that length. In addition, new extremal Type II ℤ₄-codes of length 56 are found.

Citations

• A new upper bound on the minimal distance of self-dual codes
• Shadow bounds for self-dual codes

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