TY - JOUR
T1 - Binary extremal self-dual codes of length 60 and related codes
AU - Harada, Masaaki
N1 - Funding Information:
Acknowledgements This work was supported by JSPS KAKENHI Grant Number 15H03633. The author would like to thank the anonymous reviewers for the useful comments.
Publisher Copyright:
© 2017, Springer Science+Business Media, LLC.
PY - 2018/5/1
Y1 - 2018/5/1
N2 - We give a classification of four-circulant singly even self-dual [60, 30, d] codes for d= 10 and 12. These codes are used to construct extremal singly even self-dual [60, 30, 12] codes with weight enumerator for which no extremal singly even self-dual code was previously known to exist. From extremal singly even self-dual [60, 30, 12] codes, we also construct optimal singly even self-dual [58, 29, 10] codes with weight enumerator for which no optimal singly even self-dual code was previously known to exist. Finally, we give some restriction on the possible weight enumerators of certain singly even self-dual codes with shadow of minimum weight 1.
AB - We give a classification of four-circulant singly even self-dual [60, 30, d] codes for d= 10 and 12. These codes are used to construct extremal singly even self-dual [60, 30, 12] codes with weight enumerator for which no extremal singly even self-dual code was previously known to exist. From extremal singly even self-dual [60, 30, 12] codes, we also construct optimal singly even self-dual [58, 29, 10] codes with weight enumerator for which no optimal singly even self-dual code was previously known to exist. Finally, we give some restriction on the possible weight enumerators of certain singly even self-dual codes with shadow of minimum weight 1.
KW - Extremal self-dual code
KW - Neighbor
KW - Weight enumerator
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U2 - 10.1007/s10623-017-0380-2
DO - 10.1007/s10623-017-0380-2
M3 - Article
AN - SCOPUS:85021252389
VL - 86
SP - 1085
EP - 1094
JO - Designs, Codes, and Cryptography
JF - Designs, Codes, and Cryptography
SN - 0925-1022
IS - 5
ER -