nach oben

Designs, Codes and Cryptography

Erschienen in:

10.09.2023

Classification of extremal type II \(\mathbb {Z}_4\)-codes of length 24

verfasst von: Akihiro Munemasa, Rowena Alma L. Betty

Erschienen in: Designs, Codes and Cryptography | Ausgabe 3/2024

Einloggen, um Zugang zu erhalten

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

In this paper, we give a classification of extremal Type II \(\mathbb {Z}_4\)-codes of length 24. This is equivalent to a classification of 4-frames of the Leech lattice up to the action of the automorphism group.

Vorheriger Artikel Antipodal two-weight rank metric codes

Nächster Artikel New quantum codes from self-dual codes over

Bachoc C., Bonnecaze A., Mourrain B., Solé P.: Type II codes over \(\mathbb{Z} _{4}\). IEEE Trans. Inform. Theory 43, 969–976 (1997).MathSciNetCrossRef

Bannai E., Dougherty S.T., Harada M., Oura M.: Type II codes, even unimodular lattices, and invariant rings. IEEE Trans. Inform. Theory 45, 1194–1205 (1999).MathSciNetCrossRef

Betty R.A.L., Munemasa A.: Classification of self-dual codes of length 20 over \(\mathbb{Z} _4\) and length at most 18 over \(\mathbb{F} _2+u\mathbb{F} _2\). Lecture Notes Comput. Sci. 11929, 64–77 (2019).CrossRef

Betty R.A.L., Munemasa A.: Mass formula for self-orthogonal codes over \(\mathbb{Z} _{p^2}\). J. Combin. Inform. Syst. Sci. 34, 51–66 (2009).

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

K.H. Chan, Three new methods for construction of extremal Type II \(\mathbb{Z}_{4}\)-codes. Ph.D. Thesis, University of Illinois at Chicago, Illinois, U.S.A. (2012)

Conway J.H., Sloane N.J.A.: Self-dual codes over the integers modulo 4. J. Combin. Theory Series A 62, 30–45 (1993).MathSciNetCrossRef

C. Dong, G. Mason and Y. Zhu, Discrete series of the Virasoro algebra and the moonshine module, Proceedings of Symposia in Pure Mathematics, 56 II , 295–316 (1994).

Harada M.: On the residue codes of extremal Type II \(\mathbb{Z} _{4}\)-codes of lengths 32 and 40. Discret. Math. 311, 2148–2157 (2011).CrossRef

10.

Harada M., Lam C.H., Munemasa A.: Residue codes of extremal Type II \({\mathbb{Z} }_4\)-codes and the moonshine vertex operator algebra. Mathematische Zeitschrift 274, 685–700 (2013).MathSciNetCrossRef

11.

Harada M., Munemasa A., Venkov B.: Classification of ternary extremal self-dual codes of length \(28\). Math. Comput. 78, 1787–1796 (2009).MathSciNetCrossRef

12.

Harada M., Solé P., Gaborit P.: Self-dual codes over \(\mathbb{Z} _4\) and unimodular lattices: a survey, Algebras and combinatorics (Hong Kong, 1997), 255–275. Springer, Singapore (1999).

13.

Huffman W.C.: Decompositions and extremal Type II codes over \(\mathbb{Z} _{4}\). IEEE Trans. Inform. Theory 44, 800–809 (1998).MathSciNetCrossRef

14.

Rains E.M.: Optimal self-dual codes over \(\mathbb{Z} _{4}\). Discret. Math. 203, 215–228 (1999).MathSciNetCrossRef

Titel: Classification of extremal type II -codes of length 24
verfasst von: Akihiro Munemasa
Rowena Alma L. Betty
Publikationsdatum: 10.09.2023
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 3/2024
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-023-01293-7

Springer Professional

Classification of extremal type II \(\mathbb {Z}_4\)-codes of length 24

Abstract

Premium Partner

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Weitere Artikel der Ausgabe 3/2024

Introducing nega-Forrelation: quantum algorithms in analyzing nega-Hadamard and nega-crosscorrelation spectra

Analysis and computation of multidimensional linear complexity of periodic arrays

New quantum codes from self-dual codes over

Modified Patterson–Wiedemann construction

Constructing irreducible polynomials recursively with a reverse composition method

Densities of codes of various linearity degrees in translation-invariant metric spaces

Premium Partner