Introducing two classes of optimal codes derived from one-weight FqFq[u]-additive codes

Subject Areas : Algebraic Structures and Optimization

Narjes Mohsenifar ¹ , Sadegh Sadeghi ^{2 *}

1 - Department of Electrical Engineering, Shahrekord Branch, Islamic Azad University, Shahrekord, Iran
2 - Department of Mathematics, Shahrekord Branch, Islamic Azad University, Shahrekord, Iran

Received: 2024-04-27 Accepted : 2024-06-11 Published : 2024-06-17

Keywords: Additive code, Constacyclic code, Oneweight code.,

Abstract :

Let Fq be a finite field with q elements, where q = p m, and R = Fq + uFq denotes the ring Fq[u] hu2i . For positive integers α and β, a nonempty subset C of F α q × Rβ is called an FqFq[u]-additive code if C is an Rsubmodule of F α q ×Rβ . In this paper, we obtain the generator matrix of these codes and the structure of their dual codes are given. we introduce Lee weight and homogenous weight over these codes. Also, we give some bounds on the minimum distance of these codes with respect to homogenous and Lee weights. At the end, we study one-weight codes and obtain [q 2+q, 2, q2 ] and [2(q+ 1), 2, 2q] one-weight optimal codes over Fq.

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