LCD codes and LCP of codes from units of group rings

ISSN: 1301-4048
Yayın Aralığı: Yılda 6 Sayı
Başlangıç: 1997
Yayıncı: Sakarya Üniversitesi Fen Bilimleri Enstitüsü

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

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J. L. Massey, “Linear codes with complementary duals,” Discrete Math, vol. 106, pp. 337–342, 1992.

N. Sendrier, “Linear codes with complementary duals meet the Gilbert- Varshamov bound,” Discrete Math, vol. 285, pp. 345-347, 2004.

C. Carlet and S. Guilley, S. (2016). “Complementary dual codes for countermeasures to side-channel attacks,” Adv. Math. Commun, vol. 10, pp. 131-150, 2016.

C.P. Milies, K.S. Sudarshan, “An introduction to group rings,” vol.1. Springer, Nedherlands, 2002.

P. Hurley, T. Hurley, “Codes from zerodivisors and units in group rings,” Int. J. Inf. Coding Theory vol. 1 pp. 57-87, 2009.

C. Carlet, C. Güneri, F. Özbudak, B. Özkaya, P. Solé, “On linear complementary pairs of codes”. IEEE Trans. Inform. Theory, vol. 64, pp. 6583-6589, 2018.