Coding with skew polynomial rings
نویسندگان
چکیده
In analogy to cyclic codes, we study linear codes over finite fields obtained from left ideals in a quotient ring of a (non commutative) 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 [1]. However θ-cyclic codes are performant representants of this family and we show that the dual of a θ-cyclic code is still θ-cyclic. We give many examples of self dual codes, including a [36, 18, 11] θ-cyclic code which improves the previously best know self dual code of length 36 over F4.
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ورودعنوان ژورنال:
- J. Symb. Comput.
دوره 44 شماره
صفحات -
تاریخ انتشار 2009