پديدآورندگان :
FARHANG BAFTANI FARZANEH Department of Mathematics, Ardabil Branch, Islamic Azad University, Ardabil, Iran.
كليدواژه :
Linear code , Hamming Weight , Lee Weight , Generalized Lee Weight , $(u , u+v)$ , construction of Codes
چكيده فارسي :
For a linear code $C$ of length $n$ over $Z_4$, The Lee support weight of $C$, denoted by $wt_L(C)$, is the sum of Lee weights of all columns of $A(C)$, $A(C)$ is $|C| times n$ array of all codewords in $C$. ## For $1 leq r leq rank(C)$, the $r$-th generalized Lee weight with respect to rank (GLWR) for $C$, denoted by $d_r^L(C)$, is defined as begin{equation*} d_r^L(C)=minlbrace wt_L(D); D text{ is a } Z_4-text{submodule of C}, rank(D)=rrbrace. end{equation*} Let $C_i, i=1,2$ be codes over $Z_4$ and $C$ denote $(u, u+v)$-construction of them. ##In this paper, we obtained $d_1^L(C)$ in terms of $d_1^L(C_1),d_1^L(C_2)$ and we generally obtained an upper bound for $d_r^L(C)$ for all $r$, $1 leq r leq rank(C)$.## we found a relationship between $wt_Lx$, $wt_Ly$ and $wt_L(x+y)$, for any $x, y in Z_4^n $and we showed that Lee support weight is invariant under multiplication by 3
