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ℤpℤps-additive cyclic codes are asymptotically good.
- Source :
- Cryptography & Communications; Mar2020, Vol. 12 Issue 2, p253-264, 12p
- Publication Year :
- 2020
-
Abstract
- We construct a class of ℤ p ℤ p s -additive cyclic codes generated by pairs of polynomials, where p is a prime number. The generator matrix of this class of codes is obtained. By establishing the relationship between the random ℤ p ℤ p s -additive cyclic code and random quasi-cyclic code of index 2 over ℤ p , the asymptotic properties of the rates and relative distances of this class of codes are studied. As a consequence, we prove that ℤ p ℤ p s -additive cyclic codes are asymptotically good since the asymptotic GV-bound at 1 + p s − 1 2 δ is greater than 1 2 , the relative distance of the code is convergent to δ, while the rate is convergent to 1 1 + p s − 1 for 0 < δ < 1 1 + p s − 1 . [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 19362447
- Volume :
- 12
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Cryptography & Communications
- Publication Type :
- Academic Journal
- Accession number :
- 142041516
- Full Text :
- https://doi.org/10.1007/s12095-019-00397-z