On extremal additive 𝔽 4 codes of length 10 to 18
Journal de théorie des nombres de Bordeaux, Tome 12 (2000) no. 2, pp. 255-271

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.

Dans cet article nous considérons les codes 𝔽 4 -additifs autoduaux pairs et extrémaux. Nous en donnons une classification complète en longueur 10. Avec l’hypothèse qu’au moins deux mots de poids minimal ont le même support, nous classifions les codes de longueur 14, et montrons en longueur 18 qu’un tel code est équivalent à l’unique code 𝔽 4 -linéaire hermitien autodual de paramètres [18,9,8].

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     author = {Christine Bachoc and Philippe Gaborit},
     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},
     year = {2000},
     publisher = {Universit\'e Bordeaux I},
     volume = {12},
     number = {2},
     zbl = {1007.94027},
     mrnumber = {1823184},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/item/JTNB_2000__12_2_255_0/}
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Christine Bachoc; Philippe Gaborit. 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. https://jtnb.centre-mersenne.org/item/JTNB_2000__12_2_255_0/

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