1 research outputs found

    On double cyclic codes over Z_4

    Full text link
    Let R=Z4R=\mathbb{Z}_4 be the integer ring mod 44. A double cyclic code of length (r,s)(r,s) over RR 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]R[x]-submodules of R[x]/(xrβˆ’1)Γ—R[x]/(xsβˆ’1)R[x]/(x^r-1)\times R[x]/(x^s-1). In this paper, we determine the generator polynomials of this family of codes as R[x]R[x]-submodules of R[x]/(xrβˆ’1)Γ—R[x]/(xsβˆ’1)R[x]/(x^r-1)\times R[x]/(x^s-1). Further, we also give the minimal generating sets of this family of codes as RR-submodules of R[x]/(xrβˆ’1)Γ—R[x]/(xsβˆ’1)R[x]/(x^r-1)\times R[x]/(x^s-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.Comment: 1
    corecore