Dualities over the cross product of the cyclic groups of order 2
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Tarih
2024
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
American Institute of Mathematical Sciences
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
We determine the number of symmetric dualities on the s-fold cross product of the cyclic group of order 2, which is the additive group of the finite field F2s. We show that the ratio of symmetric dualities over all dualities goes to 0 as s goes to infinity.We also prove a surprising result that given any two binary codes C and D of the same length n with |C||D| = 2n, then viewing them as groups there is a symmetric duality M with CM = D, which also relates their weight enumerators as additive codes in a group via the MacWilliams relations. Using this theorem we show that any additive code in this setting can be viewed as an additive complementary dual code of length 1 with respect to some duality.
Açıklama
Anahtar Kelimeler
Additive codes, duality, MacWilliams relations
Kaynak
Advances in Mathematics of Communications
WoS Q Değeri
Q3
Scopus Q Değeri
Cilt
18
Sayı
5
Künye
Dougherty S.T. ve Şahinkaya S. (2024).Dualities over the cross product of the cyclic groups of order 2. Advances in Mathematics of Communications, 18 (5), 1531 - 1546. DOI: 10.3934/amc.2023005
