On the Existence of Extremal Type II Z2k-Codes

2012/05/31 by Masaaki Harada, Harada, Masaaki, Tsuyoshi Miezaki +1 · 2 citations
Computer Science · Engineering · Mathematics · #94B05 (Primary) 11H71 (Secondary) 11F11 (Tertiary) #Coding theory and cryptography #Combinatorics #Combinatorics (math.CO) #Cooperative Communication and Network Coding #FOS: Mathematics #Geology #Mathematics #Number Theory (math.NT) #Paleontology #Pure mathematics #Type (biology) #graph theory and CDMA systems #math.CO #math.NT #msc:11F11 #msc:11H71 #msc:94B05

paper · pdf · doi:10.48550/arxiv.1205.6947

published in arXiv (Cornell University) (Cornell University) · 29 pages

openalex publication_date 2012/05/31 · arxiv created 2012/07/24 · arxiv updated 2012/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For lengths 8,16 and 24, it is known that there is an extremal Type II Z2k-code for every positive integer k. In this paper, we show that there is an extremal Type II Z2k-code of lengths 32,40,48,56 and 64 for every positive integer k. For length 72, it is also shown that there is an extremal Type II Z4k-code for every positive integer k with k ≥ 2.

Cited by

• On the Existence of Frames of Some Extremal Odd Unimodular Lattices and Self-Dual Zk-Codes
• Codes over Finite Ring ℤ_k, MacWilliams Identity and Theta Function

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