Main Article Content
Abstract
For group codes over elementary Abelian groups we present definitions of the generator and the parity check matrices, which are matrices over the ring of endomorphism of the group. We also lift the theorem that relates the parity check and the generator matrices of linear codes over finite fields to group codes over elementary Abelian groups. Some new codes that are MDS, self-dual, and cyclic over the Abelian group with four elements are given.
Keywords
Codes Over Groups
Elementary Abelian Groups
Endomorphism Rings.
Article Details
References
- BIGLIERI, E. and ELIA, M. 1993 Construction of linear block codes over groups. IEEE International Symposium on Information Theory, San Antonio, Texas.
- FORNEY, G.D. 1992 On the Hamming distance properties of group codes. IEEE Trans. Inform. Theory, IT-38: 1797-1801.
- FORNEY, G.D. JR. and TROTT, M.D.1993 The dynamics of group codes: state space, trellis diagram, and the canonical encoders. IEEE Trans. Inform. Theory, IT-39: 1491-1513.
- McDONALD, B.R. 1974. Finite rings with identity. Marcel Dekker, New York, 1974.
- RAN, M. and SNYDERS, J. 2000. On cyclic reversible self-dual additive codes with odd length over . IEEE Trans. Inform. Theory, IT-46: 1056-1059.
References
BIGLIERI, E. and ELIA, M. 1993 Construction of linear block codes over groups. IEEE International Symposium on Information Theory, San Antonio, Texas.
FORNEY, G.D. 1992 On the Hamming distance properties of group codes. IEEE Trans. Inform. Theory, IT-38: 1797-1801.
FORNEY, G.D. JR. and TROTT, M.D.1993 The dynamics of group codes: state space, trellis diagram, and the canonical encoders. IEEE Trans. Inform. Theory, IT-39: 1491-1513.
McDONALD, B.R. 1974. Finite rings with identity. Marcel Dekker, New York, 1974.
RAN, M. and SNYDERS, J. 2000. On cyclic reversible self-dual additive codes with odd length over . IEEE Trans. Inform. Theory, IT-46: 1056-1059.