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Fq2-double cyclic codes with respect to the Hermitian inner product.
- Source :
-
Applicable Algebra in Engineering, Communication & Computing . Mar2024, Vol. 35 Issue 2, p151-166. 16p. - Publication Year :
- 2024
-
Abstract
- In this paper, we introduce F q 2 -double cyclic codes of length n = r + s , where F q 2 is the Galois field of q 2 elements, q is a power of a prime integer p and r, s are positive integers. We determine the generator polynomials for any F q 2 -double cyclic code. For any F q 2 -double cyclic code C , we will define the Euclidean dual code C ⊥ based on the Euclidean inner product and the Hermitian dual code C ⊥ H based on the Hermitian inner product. We will construct a relationship between C ⊥ and C ⊥ H and then find the generator polynomials for the Hermitian dual code C ⊥ H. As an application of our work, we will present examples of optimal parameter linear codes over the finite field F 4 and also examples of optimal quantum codes that were derived from F 4 -double cyclic codes using the Hermitian inner product. [ABSTRACT FROM AUTHOR]
- Subjects :
- *CYCLIC codes
*LINEAR codes
*FINITE fields
Subjects
Details
- Language :
- English
- ISSN :
- 09381279
- Volume :
- 35
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Applicable Algebra in Engineering, Communication & Computing
- Publication Type :
- Academic Journal
- Accession number :
- 175567015
- Full Text :
- https://doi.org/10.1007/s00200-021-00538-z