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Applicable Algebra in Engineering, Communication and Computing
Published in:

20-07-2022 | Original Paper

On the support t-designs of extremal Type III and IV codes

Authors: Tsuyoshi Miezaki, Hiroyuki Nakasora

Published in: Applicable Algebra in Engineering, Communication and Computing | Issue 5/2024

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Abstract

Let C be an extremal Type III or IV code and \(D_{w}\) be the support design of C for weight w. We introduce the numbers, \(\delta (C)\) and s(C), as follows: \(\delta (C)\) is the largest integer t such that, for all weights, \(D_{w}\) is a t-design; s(C) denotes the largest integer t such that w exists and \(D_{w}\) is a t-design. Herein, we consider the possible values of \(\delta (C)\) and s(C).
next article Strong metric dimension in annihilating-ideal graph of commutative rings

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Literature
1.
2.
3.
Bachoc, C.: Harmonic weight enumerators of nonbinary codes and MacWilliams identities, Codes and association schemes (Piscataway, NJ, 1999), 1–23, DIMACS Series Discrete Mathematics & Theoretical Computer Science, 56, American Mathematical Society, Providence, RI (2001)
4.
Bannai, E., Koike, M., Shinohara, M., Tagami, M.: Spherical designs attached to extremal lattices and the modulo \(p\) property of Fourier coefficients of extremal modular forms. Mosc. Math. J. 6, 225–264 (2006)MathSciNetCrossRef
5.
6.
Bannai, E., Miezaki, T.: Toy models for D. H. Lehmer’s conjecture II. In: Quadratic and Higher Degree Forms, 1–27, Dev. Math., 31, Springer, New York (2013)
7.
Bannai, E., Miezaki, T., Nakasora, H.: A note on the Assmus–Mattson theorem for some binary codes II, in preparation
8.
Bannai, E., Miezaki, T., Yudin, V.A.: An elementary approach to toy models for Lehmer’s conjecture. (Russian) Izv. Ross. Akad. Nauk Ser. Mat. 75(6), 3–16 (2011). translation in Izv. Math. 75(6), 1093–1106 (2011)
9.
Brouwer, A.E.: The \(t\)-designs with \(v < 18\), Math. Centr. report ZN76, Amsterdam (Aug. 1977)
10.
Calderbank, A.R., Delsarte, P.: On error-correcting codes and invariant linear forms. SIAM J. Disc. Math. 6(1), 1–23 (1993)MathSciNetCrossRef
11.
Cameron, P.J., van Lint, J.H.: Designs, Graphs, Codes and Their Links, London Mathematical Society Student Texts, vol. 22. Cambridge University Press, Cambridge (1991)CrossRef
12.
Conway, J.H., Sloane, N.J.A.: Sphere Packings Lattices and Groups, 3rd edn. Springer, New York (1999)CrossRef
13.
14.
15.
Horiguchi, N., Miezaki, T., Nakasora, H.: On the support designs of extremal binary doubly even self-dual codes. Des. Codes Cryptogr. 72, 529–537 (2014)MathSciNetCrossRef
16.
17.
MacWilliams, F.J., Odlyzko, A.M., Sloane, N.J.A., Ward, H.N.: Self-dual codes over \(GF(4)\). J. Combin. Theory Ser. A 25, 288–318 (1978)MathSciNetCrossRef
18.
19.
20.
21.
Miezaki, T.: Design-theoretic analogies between codes, lattices, and vertex operator algebras. Des. Codes Cryptogr. 89(5), 763–780 (2021)MathSciNetCrossRef
22.
Miezaki, T., Munemasa, A., Nakasora, H.: A note on Assmus–Mattson type theorems. Des. Codes Cryptogr. 89(5), 843–858 (2021)MathSciNetCrossRef
23.
Miezaki, T., Nakasora, H.: An upper bound of the value of \(t\) of the support \(t\)-designs of extremal binary doubly even self-dual codes. Des. Codes Cryptogr. 79, 37–46 (2016)MathSciNetCrossRef
24.
Miezaki, T., Nakasora, H.: The support designs of the triply even binary codes of length \(48\). J. Combin. Des. 27, 673–681 (2019)MathSciNetCrossRef
25.
Miezaki, T., Nakasora, H.: A note on the Assmus–Mattson theorem for some binary codes. Des. Codes Cryptogr. 90(6), 1485–1502 (2022)MathSciNetCrossRef
26.
Wolfram Research, Inc., Mathematica, Version 11.2, Champaign, IL (2017)
27.
Miyamoto, M.: A new construction of the Moonshine vertex operator algebras over the real number field. Ann. Math. 159, 535–596 (2004)MathSciNetCrossRef
28.
Venkov, B.B.: Even unimodular extremal lattices (Russian), Algebraic geometry and its applications. Trudy Mat. Inst. Steklov. 165, 43–48 (1984). translation in Proc. Steklov Inst. Math. 165, 47–52 (1985)
29.
Venkov, B.B.: Réseaux et designs sphériques, (French) [Lattices and spherical designs] Réseaux euclidiens, designs sphériques et formes modulaires, 10–86, Monogr. Enseign. Math., 37, Enseignement Math., Geneva, (2001)
30.
Metadata
Title
On the support t-designs of extremal Type III and IV codes
Authors
Tsuyoshi Miezaki
Hiroyuki Nakasora
Publication date
20-07-2022
Publisher
Springer Berlin Heidelberg
Published in
Applicable Algebra in Engineering, Communication and Computing / Issue 5/2024
Print ISSN: 0938-1279
Electronic ISSN: 1432-0622
DOI
https://doi.org/10.1007/s00200-022-00571-6

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