Matrix-product codes over finite chain rings (original) (raw)
Abstract
Tim Blackmore and Graham H. Norton introduced the notion of matrix-product codes over finite fields. The present paper provides a generalization to finite chain rings. For codes a distance function is defined using a homogeneous weight function in the ring. It is proved that the minimum distance of a matrix-product codes is determined by the minimum distances of the separate codes. At the end of the paper we focus on Galois rings and define a special family of matrix-product codes.
Access this article
Subscribe and save
- Starting from 10 chapters or articles per month
- Access and download chapters and articles from more than 300k books and 2,500 journals
- Cancel anytime View plans
Buy Now
Price excludes VAT (USA)
Tax calculation will be finalised during checkout.
Instant access to the full article PDF.
Similar content being viewed by others
References
- Blackmore, T., Norton, G.H.: Matrix-Product Codes over \({\mathbb{F}_{q}}\) . AAECC 12, 477–500 (2001)
Article MATH MathSciNet Google Scholar - Hammons, A.R., Kumar, P.V., Calderbank, A.R., Sloane, N.J.A., Solé, P.: The \({\mathbb{Z}_{4}}\) -linearity of Kerdock, Preparata, Goethals, and related codes. IEEE Trans. Inform. Theory 40, 301–319 (1994)
Article MATH MathSciNet Google Scholar - van Asch, A.G., van Tilborg, H.C.A.: Two “dual” families of nearly-linear codes over \({\mathbb{Z}_{p}}\) , p odd. AAECC 11, 313–329 (2001)
Article MATH Google Scholar - Graham, H.N.: Ana Sălăgean, on the structure of linear and cyclic codes over a finite chain ring. AAECC 10, 489–506 (2000)
Article MATH Google Scholar - MacDonald, B.R.: Finite rings with identity. Dekker, New York (1974)
Google Scholar - Greferath, M., Schmidt, S.E.: Finite-ring combinatorics and MacWilliams’ Equivalence Theorem. J. Comb. Theory Ser. A 92, 17–28 (2000)
Article MATH MathSciNet Google Scholar
Author information
Authors and Affiliations
- Department of Mathematics and Computing Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands
Bram van Asch
Corresponding author
Correspondence toBram van Asch.
Rights and permissions
About this article
Cite this article
van Asch, B. Matrix-product codes over finite chain rings.AAECC 19, 39–49 (2008). https://doi.org/10.1007/s00200-008-0063-3
- Received: 29 June 2007
- Revised: 15 November 2007
- Published: 26 January 2008
- Issue date: February 2008
- DOI: https://doi.org/10.1007/s00200-008-0063-3