Journal
FINITE FIELDS AND THEIR APPLICATIONS
Volume 49, Issue -, Pages 94-107Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.ffa.2017.09.008
Keywords
Finite commutative chain ring; Affine algebra; Multivariable codes; Quasi-cyclic codes; Codes over non-chain local; Frobenius rings
Categories
Funding
- MINECO [MTM2015-65764-C3-1-P]
- Principado de Asturias Grant [GRUPIN14-142]
- [MINECO-13-MTM2013-45588-C3-1-P,]
Ask authors/readers for more resources
We consider codes defined over an affine algebra A = R[X-1,..., X-r]/< t(1)(X-1),...,t(r) (X-r)>, where t(i) (X-i) is a monic univariate polynomial over a finite commutative chain ring R. Namely, we study the A-submodules of A(l) (l is an element of N). These codes generalize both the codes over finite quotients of polynomial rings and the multivariable codes over finite chain rings. Some codes over Frobenius local rings that are not chain rings are also of this type. A canonical generator matrix for these codes is introduced with the help of the Canonical Generating System. Duality of the codes is also considered. (C) 2017 Elsevier Inc. All rights reserved.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available