Dans cet article nous considérons les codes -additifs autoduaux pairs et extrémaux. Nous en donnons une classification complète en longueur . Avec l’hypothèse qu’au moins deux mots de poids minimal ont le même support, nous classifions les codes de longueur , et montrons en longueur qu’un tel code est équivalent à l’unique code -linéaire hermitien autodual de paramètres [18,9,8].
In this paper we consider the extremal even self-dual -additive codes. We give a complete classification for length . Under the hypothesis that at least two minimal words have the same support, we classify the codes of length and we show that in length such a code is equivalent to the unique -hermitian code with parameters [18,9,8]. We construct with the help of them some extremal -modular lattices.
@article{JTNB_2000__12_2_255_0, author = {Bachoc, Christine and Gaborit, Philippe}, title = {On extremal additive $\mathbb {F}_4$ codes of length $10$ to $18$}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {255--271}, publisher = {Universit\'e Bordeaux I}, volume = {12}, number = {2}, year = {2000}, mrnumber = {1823184}, zbl = {1007.94027}, language = {en}, url = {http://archive.numdam.org/item/JTNB_2000__12_2_255_0/} }
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 SP - 255 EP - 271 VL - 12 IS - 2 PB - Université Bordeaux I UR - http://archive.numdam.org/item/JTNB_2000__12_2_255_0/ LA - en ID - JTNB_2000__12_2_255_0 ER -
%0 Journal Article %A Bachoc, Christine %A Gaborit, Philippe %T On extremal additive $\mathbb {F}_4$ codes of length $10$ to $18$ %J Journal de théorie des nombres de Bordeaux %D 2000 %P 255-271 %V 12 %N 2 %I Université Bordeaux I %U http://archive.numdam.org/item/JTNB_2000__12_2_255_0/ %G en %F JTNB_2000__12_2_255_0
Bachoc, Christine; Gaborit, Philippe. On extremal additive $\mathbb {F}_4$ codes of length $10$ to $18$. Journal de théorie des nombres de Bordeaux, Tome 12 (2000) no. 2, pp. 255-271. http://archive.numdam.org/item/JTNB_2000__12_2_255_0/
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