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Designs, Codes and Cryptography

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01.03.2016

The automorphism group of an extremal [120, 60, 24] code does not contain elements of order 29

verfasst von: Javier de la Cruz, Michael Kiermaier, Alfred Wassermann

Erschienen in: Designs, Codes and Cryptography | Ausgabe 3/2016

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Abstract

We prove that the automorphism group of an extremal binary self-dual \([120, 60, 24]\) code does not contain elements of order \(29\). Combining this with the known results in the literature, one obtains that \(|G|\) divides \(2^a\cdot 3\cdot 5\cdot 7\cdot 19\cdot 23\) for a non-negative integer \(a\).

Vorheriger Artikel Partially user-irrepressible sequence sets and conflict-avoiding codes

Nächster Artikel Weight enumerator of some irreducible cyclic codes

Assmus Jr. E.F., Mattson Jr. H.F.: New 5-designs. J. Comb. Theory 6, 122–151 (1969).

Bosma W., Cannon J., Playoust C.: The Magma algebra system. I. The user language. J. Symb. Comput. 24, 235–265 (1997).

Bouyuklieva S., de la Cruz J., Willems W.: On the automorphism group of a binary self-dual [120, 60, 24] code. AAECC 24(3–4), 201–214 (2013).

Bouyuklieva S., Malevich A., Willems W.: Automorphisms of extremal self-dual codes. IEEE Trans. Inf. Theory 56, 2091–2096 (2010).

de la Cruz J.: On extremal self-dual codes of length 120. Des. Codes Cryptogr. (2013). doi:10.1007/s10623-013-9902-8.

de la Cruz J., Willems W.: On extremal self-dual code of length 96. IEEE Trans. Inf. Theory 57, 6820–6828 (2011).

Gleason A.M.: Weight polynomials of self-dual codes and the MacWilliams identities. Actes du Congrès International des Mathèmaticiens (Nice. 1970), Tome 3, pp. 211–215. Gauthier-Villars, Paris (1971).

Grassl M.: Bounds on the minimum distance of linear codes and quantum codes [Online]. Available: http://www.codetables.de.

Huffman W.C.: Automorphisms of codes with applications to extremal doubly even codes of length 48. IEEE Trans. Inf. Theory IT- 28, 511–521 (1982).

10.

Mallows C.L., Sloane N.J.A.: An upper bound for self-dual codes. Inf. Control 22, 188–200 (1973).

11.

Pless V., Huffman W.C.: (eds.) Handbook of Coding Theory. Elsevier, Amsterdam, (1998).

12.

Sloane N.J.A.: Is there a [72, 36], \(d=16\) self-dual code? IEEE Trans. Inf. Theory 19, 251 (1973).

13.

Yorgov V.Y.: Binary self-dual codes with automorphisms of odd order, Probl. Peredachi Informatsii. vol. 19, pp. 11–24, (1983). ( in Russian).

14.

Yorgov V.Y.: A method for constructing inequivalent self-dual codes with applications to length 56. IEEE Trans. Inf. Theory IT- 33, 77–82 (1987).

15.

Yorgov V., Yorgov D.: The automorphism group of a self dual binary [72,36,16] code does not contain \(\rm Z_4\) (preprint, arXiv:1310.2570v2).

16.

Zhang S.: On the nonexistence of extremal self-dual codes. Discret. Appl. Math. 91, 277–286 (1999).

Titel: The automorphism group of an extremal [120, 60, 24] code does not contain elements of order 29
verfasst von: Javier de la Cruz
Michael Kiermaier
Alfred Wassermann
Publikationsdatum: 01.03.2016
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 3/2016
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-014-0025-7

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