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Group matrix ring codes and constructions of self-dual codes.
- Source :
-
Applicable Algebra in Engineering, Communication & Computing . Mar2023, Vol. 34 Issue 2, p279-299. 21p. - Publication Year :
- 2023
-
Abstract
- In this work, we study codes generated by elements that come from group matrix rings. We present a matrix construction which we use to generate codes in two different ambient spaces: the matrix ring M k (R) and the ring R, where R is the commutative Frobenius ring. We show that codes over the ring M k (R) are one sided ideals in the group matrix ring M k (R) G and the corresponding codes over the ring R are G k -codes of length kn. Additionally, we give a generator matrix for self-dual codes, which consist of the mentioned above matrix construction. We employ this generator matrix to search for binary self-dual codes with parameters [72, 36, 12] and find new singly-even and doubly-even codes of this type. In particular, we construct 16 new Type I and 4 new Type II binary [72, 36, 12] self-dual codes. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09381279
- Volume :
- 34
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Applicable Algebra in Engineering, Communication & Computing
- Publication Type :
- Academic Journal
- Accession number :
- 162013716
- Full Text :
- https://doi.org/10.1007/s00200-021-00504-9