@article{ee78b9c6df51471a93863fdd84d2dcf3,
title = "On ZpZpk-additive codes and their duality",
abstract = "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. ",
keywords = "Additives, Advanced Video Coding (AVC), Binary codes, compression artifacts, convolutional neural networks (CNN), Generators, High Efficiency Video Coding (HEVC), Linear codes, Measurement, Propulsion, video compression, Zinc, linear codes, Gray map, MacWilliams identity, two-weight codes, 1-perfect codes, Dual codes",
author = "Minjia Shi and Rongsheng Wu and Krotov, {Denis S.}",
note = "Funding Information: This work was supported in part by the National Natural Science Foundation of China under Grant 61672036, in part by the Excellent Youth Foundation of Natural Science Foundation of Anhui Province under Grant 1808085J20, and in part by the Russian Academy of Sciences, Siberian Branch, through the Program for Fundamental Scientific Studies under Grant 0314-2016-0016. Funding Information: Manuscript received August 23, 2018; revised October 27, 2018; accepted November 22, 2018. Date of publication November 30, 2018; date of current version May 20, 2019. This work was supported in part by the National Natural Science Foundation of China under Grant 61672036, in part by the Excellent Youth Foundation of Natural Science Foundation of Anhui Province under Grant 1808085J20, and in part by the Russian Academy of Sciences, Siberian Branch, through the Program for Fundamental Scientific Studies under Grant 0314-2016-0016. Publisher Copyright: {\textcopyright} 1963-2012 IEEE. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.",
year = "2019",
month = jun,
day = "1",
doi = "10.1109/TIT.2018.2883759",
language = "English",
volume = "65",
pages = "3841--3847",
journal = "IEEE Transactions on Information Theory",
issn = "0018-9448",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "6",
}