Title :
A family of highly symmetric codes
Author :
Bierbrauer, Jürgen ; Marcugini, Stefano ; Pambianco, Fernanda
Author_Institution :
Dept. of Math. Sci., Michigan Technol. Univ., Houghton, MI, USA
Abstract :
We define a class of codes admitting a large automorphism group. This family contains the binary extended Hamming code, the hexacode, the Golay codes, the Pless symmetry codes, as well as the [16,4,12]8-codes constructed by Marcugini et al. A computer search resulted in the construction of codes with new parameters [28,7,18]8,[32,8,20]8, and [39,13,17]4 belonging to this family.
Keywords :
Galois fields; Golay codes; Hamming codes; binary codes; group codes; linear codes; Galois field; Golay code; Pless symmetry code; automorphism group; binary extended Hamming code; hexacode; highly symmetric code; linear code; Galois fields; Geometry; Informatics; Linear code; Mathematics; Orbits; Symmetric matrices; Galois fields; Linear codes; symmetry groups;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2005.855607
