On $Z_p Z_{p^k}$ -Additive Codes and Their Duality Full article
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IEEE Transactions on Information Theory
ISSN: 0018-9448 , E-ISSN: 1557-9654 |
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| Output data | Year: 2019, Volume: 65, Number: 6, Pages: 3841-3847 Pages count : 7 DOI: 10.1109/tit.2018.2883759 | ||||||
| Tags | Dual codes, Gray map, linear codes, MacWilliams identity, two-weight codes, 1-perfect codes | ||||||
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Abstract:
In this paper, two different Gray-like maps from Zpα × Zpkβ, where p is prime, to Zpn , n=αtβpk-1 , denoted by φ and Φ, respectively, are presented. We have determined the connection between the weight enumerators among the image codes under these two mappings. We show that if C is a Zp Zpk-additive code, and C* is its dual, then the weight enumerators of the image p-ary codes φ(C) and Φ(C*) are formally dual. This is a partial generalization of [D. S. Krotov, On Z2k-dual binary codes, IEEE Transactions Information Theory 53 (2007), 1532-1537], and the result is generalized to odd characteristic p and mixed alphabet. In addition, a construction of 1-perfect additive codes in the mixed Zp Zp2 ... Zpk alphabet is given.
Cite:
Shi M.
, Wu R.
, Krotov D.S.
On $Z_p Z_{p^k}$ -Additive Codes and Their Duality
IEEE Transactions on Information Theory. 2019. V.65. N6. P.3841-3847. DOI: 10.1109/tit.2018.2883759 WOS Scopus РИНЦ OpenAlex
On $Z_p Z_{p^k}$ -Additive Codes and Their Duality
IEEE Transactions on Information Theory. 2019. V.65. N6. P.3841-3847. DOI: 10.1109/tit.2018.2883759 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Aug 23, 2018 |
| Accepted: | Nov 22, 2018 |
| Published online: | Nov 30, 2018 |
Identifiers:
| Web of science: | WOS:000468433400032 |
| Scopus: | 2-s2.0-85057805645 |
| Elibrary: | 41621162 |
| OpenAlex: | W2889940767 |