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- W2734264218 abstract "Let $F_p$ be the prime field with $p$ elements. We derive the homogeneous weight on the Frobenius matrix ring $M_2(F_p)$ in terms of the generating character. We also give a generalization of the Lee weight on the finite chain ring $F_{p^2}+uF_{p^2}$ where $u^2=0$. A non-commutative ring, denoted by $mathcal{F}_{p^2}+mathbf{v}_p mathcal{F}_{p^2}$, $mathbf{v}_p$ an involution in $M_2(F_p)$, that is isomorphic to $M_2(F_p)$ and is a left $F_{p^2}$-vector space, is constructed through a unital embedding $tau$ from $F_{p^2}$ to $M_2(F_p)$. The elements of $mathcal{F}_{p^2}$ come from $M_2(F_p)$ such that $tau(F_{p^2})=mathcal{F}_{p^2}$. The irreducible polynomial $f(x)=x^2+x+(p-1) in F_p[x]$ required in $tau$ restricts our study of cyclic codes over $M_2(F_p)$ endowed with the Bachoc weight to the case $pequiv$ $2$ or $3$ mod $5$. The images of these codes via a left $F_p$-module isometry are additive cyclic codes over $F_{p^2}+uF_{p^2}$ endowed with the Lee weight. New examples of such codes are given." @default.
- W2734264218 created "2017-07-14" @default.
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- W2734264218 creator A5039168367 @default.
- W2734264218 date "2014-09-25" @default.
- W2734264218 modified "2023-09-27" @default.
- W2734264218 title "Cyclic Codes over the Matrix Ring $M_2(F_p)$ and Their Isometric Images over $F_{p^2}+uF_{p^2}$" @default.
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