TY - JOUR
T1 - On the support t-designs of extremal Type III and IV codes
AU - Miezaki, Tsuyoshi
AU - Nakasora, Hiroyuki
N1 - Funding Information:
The authors would also like to thank the anonymous reviewers for their beneficial comments on an earlier version of the manuscript. The first named author is supported by JSPS KAKENHI (22K03277).
Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2022
Y1 - 2022
N2 - Let C be an extremal Type III or IV code and Dw be the support design of C for weight w. We introduce the numbers, δ(C) and s(C), as follows: δ(C) is the largest integer t such that, for all weights, Dw is a t-design; s(C) denotes the largest integer t such that w exists and Dw is a t-design. Herein, we consider the possible values of δ(C) and s(C).
AB - Let C be an extremal Type III or IV code and Dw be the support design of C for weight w. We introduce the numbers, δ(C) and s(C), as follows: δ(C) is the largest integer t such that, for all weights, Dw is a t-design; s(C) denotes the largest integer t such that w exists and Dw is a t-design. Herein, we consider the possible values of δ(C) and s(C).
KW - Assmus–Mattson theorem
KW - Harmonic weight enumerators
KW - Self-dual codes
KW - t-designs
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U2 - 10.1007/s00200-022-00571-6
DO - 10.1007/s00200-022-00571-6
M3 - Article
AN - SCOPUS:85134568930
SN - 0938-1279
JO - Applicable Algebra in Engineering, Communications and Computing
JF - Applicable Algebra in Engineering, Communications and Computing
ER -