On the equivalence of cyclic and quasi-cyclic codes over finite fields
نویسندگان
چکیده
This paper studies the equivalence problem for cyclic codes of length p and quasi-cyclic codes of length pl. In particular, we generalize the results of Huffman, Job, and Pless (J. Combin. Theory. A, 62, 183–215, 1993), who considered the special case p. This is achieved by explicitly giving the permutations by which two cyclic codes of prime power length are equivalent. This allows us to obtain an algorithm which solves the problem of equivalency for cyclic codes of length p in polynomial time. Further, we characterize the set by which two quasi-cyclic codes of length pl can be equivalent, and prove that the affine group is one of its subsets. 2010 MSC: 94B05, 94B15, 94B60
منابع مشابه
Equivalence of Quasi-cyclic Codes over Finite Fields
This paper considers the equivalence problem for quasi-cyclic codes over finite fields. The results obtained are used to construct isodual quasi-cyclic codes.
متن کاملThe Permutation Groups and the Equivalence of Cyclic and Quasi-Cyclic Codes
We give the class of finite groups which arise as the permutation groups of cyclic codes over finite fields. Furthermore, we extend the results of Brand and Huffman et al. and we find the properties of the set of permutations by which two cyclic codes of length p can be equivalent. We also find the set of permutations by which two quasi-cyclic codes can be equivalent.
متن کاملOn Skew Cyclic Codes over a Finite Ring
In this paper, we classify the skew cyclic codes over Fp + vF_p + v^2F_p, where p is a prime number and v^3 = v. Each skew cyclic code is a F_p+vF_p+v^2F_p-submodule of the (F_p+vF_p+v^2F_p)[x;alpha], where v^3 = v and alpha(v) = -v. Also, we give an explicit forms for the generator of these codes. Moreover, an algorithm of encoding and decoding for these codes is presented.
متن کاملSkew Generalized Quasi-Cyclic Codes Over Finite Fields
In this work, we study a class of generalized quasi-cyclic (GQC) codes called skew GQC codes. By the factorization theory of ideals, we give the Chinese Remainder Theorem over the skew polynomial ring, which leads to a canonical decomposition of skew GQC codes. We also focus on some characteristics of skew GQC codes in details. For a 1-generator skew GQC code, we define the parity-check polynom...
متن کاملQuasi-cyclic codes as codes over rings of matrices
Quasi cyclic codes over a finite field are viewed as cyclic codes over a non commutative ring of matrices over a finite field. This point of view permits to generalize some known results about linear recurring sequences and to propose a new construction of some quasi cyclic codes and self dual codes.
متن کامل