arXiv subjects
Publications and source records attributed to Noor Mohammad Khan.
In this study, linear codes having their Lee-weight distributions over the semi-local ring $\mathbb{F}_{q}+u\mathbb{F}_{q}$ with $u^{2}=1$ are constructed using the defining set and Gauss sums for an odd prime $q $. Moreover, we derive complete Hamming-weight enumerators for the images of the constructed linear codes under the Gray map. We finally show an application to secret sharing schemes.
For any positive integer $m$ and an odd prime $p$; let $\mathbb{F}_{q}+u\mathbb{F}_{q}$, where $q=p^{m}$, be a ring extension of the ring $\mathbb{F}_{p}+u\mathbb{F}_{p}.$ In this paper, we construct linear codes over $\mathbb{F}_{p}+u\mathbb{F}_{p}$ by using trace function defined on $\mathbb{F}_{q}+u\mathbb{F}_{q}$ and determine their Hamming weight distributions by employing symplectic-weight distributions of their Gray images.
In the present paper, a series of results and examples that explore the structural features of H-commutative semigroups are provided. We also generalise a result of Isbell from commutative semigroups to H-commutative semigroups by showing that the dominion of an H-commutative semigroup is H-commutative. We then use this to generalise Howie and Isbell's result that any H-commutative semigroup satisfying the minimum condition on principal ideals is saturated.