LCD codes and LCP of codes from units of group rings

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Atıf İçin Kopyala

KOROGLU M. E.

Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, cilt.23, sa.3, ss.486-492, 2019 (Hakemli Dergi)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 23 Sayı: 3
• Basım Tarihi: 2019
• Doi Numarası: 10.16984/saufenbilder.459123
• Dergi Adı: Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi
• Derginin Tarandığı İndeksler: TR DİZİN (ULAKBİM)
• Sayfa Sayıları: ss.486-492
• Yıldız Teknik Üniversitesi Adresli: Evet

Özet

A linear code with complementary dual (LCD) is a linear code such that CC  0. LCD codes are ofgreat importance due to their wide range of applications in consumer electronics, storage systems andcryptography. Group rings have a rich source of units. Also the well-known structural linear codes such ascyclic codes are within the family of group ring codes. Thus, group rings offer an affluent source forstructural codes that may lead to linear codes with good properties. In this work, we derive a condition forcodes obtained from units of group rings to be LCD. We show that a special decomposition of group ringsmeet the LCD condition. We also proposed a consruction of linear complementary pair (LCP) of codes.