TY - JOUR
T1 - On a 5-design related to a putative extremal doubly even self-dual code of length a multiple of 24
AU - Harada, Masaaki
N1 - Funding Information:
The author would like to thank Tsuyoshi Miezaki for verifying the calculations in the proofs of Propositions 6 and 7, independently. This work is supported by JSPS KAKENHI Grant Number 23340021. This work was partially carried out at Yamagata University.
Publisher Copyright:
© 2014, Springer Science+Business Media New York.
PY - 2015/9/6
Y1 - 2015/9/6
N2 - 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 (Formula presented) and (Formula presented.), then it is shown that an extremal doubly even self-dual code of length 24m is generated by codewords of weight 4k.
AB - 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 (Formula presented) and (Formula presented.), then it is shown that an extremal doubly even self-dual code of length 24m is generated by codewords of weight 4k.
KW - Extremal doubly even Self-dual code
KW - Self-orthogonal (Formula presented.)-design
KW - Weight enumerator
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U2 - 10.1007/s10623-014-9963-3
DO - 10.1007/s10623-014-9963-3
M3 - Article
AN - SCOPUS:84938581783
SN - 0925-1022
VL - 76
SP - 373
EP - 384
JO - Designs, Codes, and Cryptography
JF - Designs, Codes, and Cryptography
IS - 3
ER -