论文标题
关于在订单4的非积极环上的代码分类
On the Classification of Codes over Non-Unital Ring of Order 4
论文作者
论文摘要
在过去的60年中，编码理论已通过有限字段进行了很多研究，$ \ mathbb {f} _q $或交换戒指$ \ MATHCAL {R} $ at unity。尽管以1993美元的价格进行了一项关于订单$ p^2 $的环（不一定是统一或统一性的戒指）的研究，但两年前仅在两年前就浮出水面的非交换环或非交通性的非连续性环的构造。 In this letter, we extend the diverse research on exploring the codes over the non-commutative and non-unital ring $E= \langle 2a=2b=0, a^2=a, b^2=b, ab=a, ba=b \rangle$ by presenting the classification of optimal and nice codes of length $n\leq7$ over $E$, along-with respective weight enumerators and complete weight enumerators.
In the last 60 years coding theory has been studied a lot over finite fields $\mathbb{F}_q$ or commutative rings $\mathcal{R}$ with unity. Although in $1993$, a study on the classification of the rings (not necessarily commutative or ring with unity) of order $p^2$ had been presented, the construction of codes over non-commutative rings or non-commutative non-unital rings surfaced merely two years ago. In this letter, we extend the diverse research on exploring the codes over the non-commutative and non-unital ring $E= \langle 2a=2b=0, a^2=a, b^2=b, ab=a, ba=b \rangle$ by presenting the classification of optimal and nice codes of length $n\leq7$ over $E$, along-with respective weight enumerators and complete weight enumerators.
