Higher Power Residue Codes

Authors:
Robin Chapman
Affiliations:
Department of Mathematics, University of Exeter, Exeter, EX4 4QE, United Kingdomf1rjc@maths.exeter.ac.ukf1
Venue:
Finite Fields and Their Applications
Year:
1997

Citing 2
Cited 1

Reconstructing the ternary Golay code

Journal of Combinatorial Theory Series A
Quaternary quadratic residue codes and unimodular lattices

IEEE Transactions on Information Theory

Higher Power Residue Codes and the Leech Lattice

Journal of Algebraic Combinatorics: An International Journal

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Abstract

For certain primeslandp, and characters @g:F*"p-F*"l"^"2, we construct codesWof lengthp+ 1 overF"l"^"2which are linear overF"l, but not overF"l"^"2, and which are invariant under a monomial action of the group SL(2,p). We consider the cases of cubic and quartic characters in detail and use theWto construct linear codes overF"lin these cases.