Back to Search
Start Over
Z4Z4Z4-additive cyclic codes are asymptotically good.
- Source :
-
Applicable Algebra in Engineering, Communication & Computing . Jul2024, Vol. 35 Issue 4, p485-505. 21p. - Publication Year :
- 2024
-
Abstract
- In this paper, we construct a class of Z 4 Z 4 Z 4 -additive cyclic codes generated by 3-tuples of polynomials. We discuss their algebraic structure and show that generator matrices can be constructed for all codes in this class. We study asymptotic properties of this class of codes by using a Bernoulli random variable. Moreover, let 0 < δ < 1 be a real number such that the entropy h 4 ((k + l + t) δ 6) < 1 4 , we show that the relative minimum distance converges to δ and the rate of the random codes converges to 1 k + l + t , where k, l, and t are pairwise co-prime positive odd integers. Finally, we conclude that the Z 4 Z 4 Z 4 -additive cyclic codes are asymptotically good. [ABSTRACT FROM AUTHOR]
- Subjects :
- *CYCLIC codes
*REAL numbers
*RANDOM variables
Subjects
Details
- Language :
- English
- ISSN :
- 09381279
- Volume :
- 35
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Applicable Algebra in Engineering, Communication & Computing
- Publication Type :
- Academic Journal
- Accession number :
- 177817874
- Full Text :
- https://doi.org/10.1007/s00200-022-00557-4