Details:
Title  Coding with skew polynomial rings  Author(s)  Delphine Boucher, Felix Ulmer  Type  Article in Journal  Abstract  In analogy to cyclic codes, we study linear codes over finite fields obtained from left ideals in a quotient ring of a (noncommutative) skew polynomial ring. The paper shows how existence and properties of such codes are linked to arithmetic properties of skew polynomials. This class of codes is a generalization of the θ cyclic codes discussed in [Boucher, D., Geiselmann, W., Ulmer, F., 2007. Skew cyclic codes. Applied Algebra in Engineering, Communication and Computing 18, 379–389]. However θ cyclic codes are powerful representatives of this family and we show that the dual of a θ cyclic code is still θ cyclic. Using Groebner bases, we compute all Euclidean and Hermitian selfdual θ cyclic codes over F 4 of length less than 40, including a[36,18,11] Euclidean selfdual θ cyclic code which improves the previously best known selfdual code of length 36 over F 4 .  Keywords  Cyclic codes, Finite rings, Skew polynomial rings  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717108001788 
Language  English  Journal  Journal of Symbolic Computation  Volume  44  Number  12  Pages  1644  1656  Year  2009  Note  Gröbner Bases in Cryptography, Coding Theory, and Algebraic Combinatorics  Edition  0  Translation 
No  Refereed 
No 
