학술논문
Some skew constacyclic codes over $\Bbb{F}_q+u\Bbb{F}_q$.
Document Type
Journal
Author
Hebbache, Z. (DZ-BOUMM) AMS Author Profile; Guenda, K. (DZ-BOUMM) AMS Author Profile; Özzaim, N. T. (TR-TUBT) AMS Author Profile; Özen, M. (TR-SAKU) AMS Author Profile; Gulliver, T. A. (3-VCTR-EN) AMS Author Profile
Source
Subject
94 Information and communication, circuits -- 94B Theory of error-correcting codes and error-detecting codes
94B15Cyclic codes
94B15
Language
English
Abstract
In this paper, the authors study the existence of self-dual skew cyclic and negacyclic codes generated by skew binomials of odd characteristic over the finite chain ring $R = \Bbb F_q +u\Bbb F_q$ with $u^2 = 0$. They also extend an algorithm of Boucher and Ulmer given in 2014 to construct self-dual skew cyclic and skew negacyclic codes based on the least common left multiples of non-commutative polynomials over $\Bbb F_q +u\Bbb F_q$. Furthermore, they give conditions on the existence of LCD skew cyclic and skew negacyclic codes. Finally, they provide some examples of skew constacyclic and LCD codes over $R$.