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Title:
New self-orthogonal codes from weakly regular plateaued functions and their application in LCD codes
Authors: Melike Çakmak, Ahmet Sınak, Oğuz Yayla
Abstract:A linear code is considered self-orthogonal if it is contained within its dual code. Self-orthogonal codes have applications in linear complementary dual codes, quantum codes and so on. The construction of self-orthogonal codes from functions over finite fields has been studied in the literature. In this paper, we generalize the construction method given by Heng et al. (2023) to weakly regular plateaued functions. We first construct several families of ternary self-orthogonal codes from weakly regular plateaued unbalanced functions. Then we use the self-orthogonal codes to construct new families of ternary LCD codes. As a consequence, we obtain (almost) optimal ternary self-orthogonal codes and LCD codes. Moreover, we propose two new classes of p-ary linear codes from weakly regular plateaued unbalanced functions over the finite fields of odd characteristics.
ePrint: https://eprint.iacr.org/2024/125
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