TY - JOUR

T1 - An upper bound of the value of t of the support t-designs of extremal binary doubly even self-dual codes

AU - Miezaki, Tsuyoshi

AU - Nakasora, Hiroyuki

N1 - Funding Information:
The authors wish to thank Masaaki Kitazume for helpful discussions in Chiba University. The authors also thank Eiichi Bannai for providing the reference []. The second author would like to thank Masaaki Harada for useful discussions in Tohoku University. This work was supported by JSPS KAKENHI (22840003, 24740031).
Publisher Copyright:
© 2015, Springer Science+Business Media New York.

PY - 2016/4/1

Y1 - 2016/4/1

N2 - Let (Formula presented.) be an extremal binary doubly even self-dual code of length (Formula presented.) and (Formula presented.) be the support design of (Formula presented.) for a weight (Formula presented.). We introduce the two numbers (Formula presented.) and (Formula presented.) : (Formula presented.) is the largest integer (Formula presented.) such that, for all wight, (Formula presented.) is a (Formula presented.) -design; (Formula presented.) denotes the largest integer (Formula presented.) such that there exists a (Formula presented.) such that (Formula presented.) is a (Formula presented.) -design. In this paper, we consider the possible values of (Formula presented.) and (Formula presented.).

AB - Let (Formula presented.) be an extremal binary doubly even self-dual code of length (Formula presented.) and (Formula presented.) be the support design of (Formula presented.) for a weight (Formula presented.). We introduce the two numbers (Formula presented.) and (Formula presented.) : (Formula presented.) is the largest integer (Formula presented.) such that, for all wight, (Formula presented.) is a (Formula presented.) -design; (Formula presented.) denotes the largest integer (Formula presented.) such that there exists a (Formula presented.) such that (Formula presented.) is a (Formula presented.) -design. In this paper, we consider the possible values of (Formula presented.) and (Formula presented.).

KW - Assmus–Mattson theorem

KW - Harmonic weight enumerators

KW - Self-dual codes

KW - t-Designs

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U2 - 10.1007/s10623-014-0033-7

DO - 10.1007/s10623-014-0033-7

M3 - Article

AN - SCOPUS:84960330129

SN - 0925-1022

VL - 79

SP - 37

EP - 46

JO - Designs, Codes, and Cryptography

JF - Designs, Codes, and Cryptography

IS - 1

ER -