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On the duals of quasi-cyclic codes and their application to quantum codes.
- Source :
-
Quantum Information Processing . Apr2024, Vol. 23 Issue 4, p1-26. 26p. - Publication Year :
- 2024
-
Abstract
- This paper presents some results on 1-generator quasi-cyclic (QC) codes and their duals over finite fields. We have explicitly obtained a set of generators for the dual of a 1-generator QC code C from the generator of C, for some restricted cases. From the form of the generators of the dual code C ⊥ , we have derived upper bounds on the minimum distance of C ⊥ . For their applications in constructing quantum codes, we have presented some criteria for 1-generator QC codes to be self-orthogonal or self-dual. Then using the CSS construction, we have obtained some new and better quantum codes with the help of self-orthogonal 1-generator QC codes. [ABSTRACT FROM AUTHOR]
- Subjects :
- *CYCLIC codes
*CODE generators
*FINITE fields
Subjects
Details
- Language :
- English
- ISSN :
- 15700755
- Volume :
- 23
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Quantum Information Processing
- Publication Type :
- Academic Journal
- Accession number :
- 177112097
- Full Text :
- https://doi.org/10.1007/s11128-024-04318-9