On double cyclic codes over Z4
نویسندگان
چکیده
Let R = Z4 be the integer ring mod 4. A double cyclic code of length (r, s) over R is a set that can be partitioned into two parts that any cyclic shift of the coordinates of both parts leaves invariant the code. These codes can be viewed as R[x]-submodules of R[x]/(xr −1)×R[x]/(xs−1). In this paper, we determine the generator polynomials of this family of codes as R[x]-submodules of R[x]/(xr − 1) × R[x]/(xs − 1). Further, we also give the minimal generating sets of this family of codes as R-submodules of R[x]/(xr − 1)×R[x]/(xs − 1). Some optimal or suboptimal nonlinear binary codes are obtained from this family of codes. Finally, we determine the relationship of generators between the double cyclic code and its dual.
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ورودعنوان ژورنال:
- Finite Fields and Their Applications
دوره 39 شماره
صفحات -
تاریخ انتشار 2016