TY - JOUR
T1 - Singly even self-dual codes of length 24k + 10 and minimum weight 4k + 2
AU - Harada, Masaaki
N1 - Funding Information:
Acknowledgments This work was supported by JSPS KAKENHI Grant Number 15H03633. The author would like to thank the anonymous referee for useful comments.
Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2019/7/15
Y1 - 2019/7/15
N2 - Currently, the existence of an extremal singly even self-dual code of length 24k + 10 is unknown for all nonnegative integers k. In this note, we study singly even self-dual [24k + 10, 12k + 5, 4k + 2] codes. We give some restrictions on the possible weight enumerators of singly even self-dual [24k + 10, 12k + 5, 4k + 2] codes with shadows of minimum weight at least 5 for k = 2, 3, 4, 5. We discuss a method for constructing singly even self-dual codes with minimal shadow. As an example, a singly even self-dual [82, 41, 14] code with minimal shadow is constructed for the first time. In addition, as neighbors of the code, we construct singly even self-dual [82, 41, 14] codes with weight enumerator for which no singly even self-dual code was previously known to exist.
AB - Currently, the existence of an extremal singly even self-dual code of length 24k + 10 is unknown for all nonnegative integers k. In this note, we study singly even self-dual [24k + 10, 12k + 5, 4k + 2] codes. We give some restrictions on the possible weight enumerators of singly even self-dual [24k + 10, 12k + 5, 4k + 2] codes with shadows of minimum weight at least 5 for k = 2, 3, 4, 5. We discuss a method for constructing singly even self-dual codes with minimal shadow. As an example, a singly even self-dual [82, 41, 14] code with minimal shadow is constructed for the first time. In addition, as neighbors of the code, we construct singly even self-dual [82, 41, 14] codes with weight enumerator for which no singly even self-dual code was previously known to exist.
KW - Self-dual code
KW - Shadow
KW - Weight enumerator
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U2 - 10.1007/s12095-018-0303-8
DO - 10.1007/s12095-018-0303-8
M3 - Article
AN - SCOPUS:85068141990
VL - 11
SP - 597
EP - 608
JO - Cryptography and Communications
JF - Cryptography and Communications
SN - 1936-2447
IS - 4
ER -