On ZpZpk-additive codes and their duality

Minjia Shi, Rongsheng Wu, Denis S. Krotov

Результат исследования: Научные публикации в периодических изданияхстатья

5 Цитирования (Scopus)


In this paper, two different Gray-like maps from Z p α × Z pk β , where p is prime, to Z p n , n=α +β p k-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 Z p Z p k -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 Z 2 k -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 Z p Z p 2 ⋯ Z p k alphabet is given.

Язык оригиналаанглийский
Номер статьи8554305
Страницы (с-по)3841-3847
Число страниц7
ЖурналIEEE Transactions on Information Theory
Номер выпуска6
СостояниеОпубликовано - 1 июн 2019

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