On extremal additive 𝔽 4 codes of length 10 to 18

Christine Bachoc; Philippe Gaborit

Journal de théorie des nombres de Bordeaux (2000)

  • Volume: 12, Issue: 2, page 255-271
  • ISSN: 1246-7405

Abstract

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In this paper we consider the extremal even self-dual 𝔽 4 -additive codes. We give a complete classification for length 10 . Under the hypothesis that at least two minimal words have the same support, we classify the codes of length 14 and we show that in length 18 such a code is equivalent to the unique 𝔽 4 -hermitian code with parameters [18,9,8]. We construct with the help of them some extremal 3 -modular lattices.

How to cite

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Bachoc, Christine, and Gaborit, Philippe. "On extremal additive $\mathbb {F}_4$ codes of length $10$ to $18$." Journal de théorie des nombres de Bordeaux 12.2 (2000): 255-271. <http://eudml.org/doc/248496>.

@article{Bachoc2000,
abstract = {In this paper we consider the extremal even self-dual $\mathbb \{F\}_4$-additive codes. We give a complete classification for length $10$. Under the hypothesis that at least two minimal words have the same support, we classify the codes of length $14$ and we show that in length $18$ such a code is equivalent to the unique $\mathbb \{F\}_4$-hermitian code with parameters [18,9,8]. We construct with the help of them some extremal $3$-modular lattices.},
author = {Bachoc, Christine, Gaborit, Philippe},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {additive code; self-dual code; extremal code},
language = {eng},
number = {2},
pages = {255-271},
publisher = {Université Bordeaux I},
title = {On extremal additive $\mathbb \{F\}_4$ codes of length $10$ to $18$},
url = {http://eudml.org/doc/248496},
volume = {12},
year = {2000},
}

TY - JOUR
AU - Bachoc, Christine
AU - Gaborit, Philippe
TI - On extremal additive $\mathbb {F}_4$ codes of length $10$ to $18$
JO - Journal de théorie des nombres de Bordeaux
PY - 2000
PB - Université Bordeaux I
VL - 12
IS - 2
SP - 255
EP - 271
AB - In this paper we consider the extremal even self-dual $\mathbb {F}_4$-additive codes. We give a complete classification for length $10$. Under the hypothesis that at least two minimal words have the same support, we classify the codes of length $14$ and we show that in length $18$ such a code is equivalent to the unique $\mathbb {F}_4$-hermitian code with parameters [18,9,8]. We construct with the help of them some extremal $3$-modular lattices.
LA - eng
KW - additive code; self-dual code; extremal code
UR - http://eudml.org/doc/248496
ER -

References

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  9. [9] F.J. Macwilliams, A.M. Odlyzko, N.J.A. Sloane, H.N. Ward, Self-Dual Codes over GF(4). J. Comb. Theory25 (1978), 288-318. Zbl0397.94013MR514624
  10. [10] G. Nebe, Finite subgroups of GL(24, Q). Exp. Math.5 (1996), 2341-2397. Zbl0856.20031MR1390378
  11. [11] H.-G. Quebbemann, Modular Lattices in Euclidean Spaces. J. Number Theory54 (1995), 190-202. Zbl0874.11038MR1354045
  12. [12] E.M. Rains, N.J.A. Sloane, Self-dual codes. In: Handbook of Coding Theory, ed. V. S. Pless and W. C. Huffman. Amsterdam: Elsevier, 1998, pp. 177-294. Zbl0936.94017MR1667939
  13. [13] R. Scharlau, R. Schulze-Pillot, Extremal Lattices, Algorithmic Algebra and Number Theory (Heidelberg1997), 139-170, Springer, Berlin, 1999. Zbl0944.11012MR1672117

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