English

Linear Codes over Z_4+uZ_4: MacWilliams identities, projections, and formally self-dual codes

Rings and Algebras 2013-07-12 v1 Information Theory math.IT

Abstract

Linear codes are considered over the ring Z_4+uZ_4, a non-chain extension of Z_4. Lee weights, Gray maps for these codes are defined and MacWilliams identities for the complete, symmetrized and Lee weight enumerators are proved. Two projections from Z_4+uZ_4 to the rings Z_4 and F_2+uF_2 are considered and self-dual codes over Z_4+uZ_4 are studied in connection with these projections. Finally three constructions are given for formally self-dual codes over Z_4+uZ_4 and their Z_4-images together with some good examples of formally self-dual Z_4-codes obtained through these constructions.

Keywords

Cite

@article{arxiv.1307.3047,
  title  = {Linear Codes over Z_4+uZ_4: MacWilliams identities, projections, and formally self-dual codes},
  author = {Bahattin Yildiz and Suat Karadeniz},
  journal= {arXiv preprint arXiv:1307.3047},
  year   = {2013}
}

Comments

12 pages. Partially presented in the 13th International Workshop on Algebraic and combinatorial coding theory, Pomorie, Bulgaria, 2012