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Designs, Codes and Cryptography

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01-09-2015

On a 5-design related to a putative extremal doubly even self-dual code of length a multiple of 24

Author: Masaaki Harada

Published in: Designs, Codes and Cryptography | Issue 3/2015

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Abstract

By the Assmus and Mattson theorem, the codewords of each nontrivial weight in an extremal doubly even self-dual code of length 24m form a self-orthogonal 5-design. In this paper, we study the codes constructed from self-orthogonal 5-designs with the same parameters as the above 5-designs. We give some parameters of a self-orthogonal 5-design whose existence is equivalent to that of an extremal doubly even self-dual code of length 24m for \(m=3,4,5,6\). If \(m \in \{1,\ldots ,6\}\), \(k \in \{m+1,\ldots ,5m-1\}\) and \((m,k) \ne (6,18)\), then it is shown that an extremal doubly even self-dual code of length 24m is generated by codewords of weight \(4k\).

next article Differential cryptanalysis of PRESENT-like cipher

See Sects. 3 and 4 for the marks \(*\) in Table 1.

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Title: On a 5-design related to a putative extremal doubly even self-dual code of length a multiple of 24
Author: Masaaki Harada
Publication date: 01-09-2015
Publisher: Springer US
Published in: Designs, Codes and Cryptography / Issue 3/2015
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-014-9963-3

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On a 5-design related to a putative extremal doubly even self-dual code of length a multiple of 24

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