On the Classification of Codes over Non-Unital Ring of Order 4

08/18/2022

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by   Sourav Deb, et al.

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In the last 60 years coding theory has been studied a lot over finite fields 𝔽_q or commutative rings 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= ⟨ 2a=2b=0, a^2=a, b^2=b, ab=a, ba=b ⟩ by presenting the classification of optimal and nice codes of length n≤7 over E, along-with respective weight enumerators and complete weight enumerators.