Reversible Self-Dual Codes over Finite Field

Abstract

Reversible self-dual code is a linear code which combine the properties from self-dual code and reversible code. Previous research shows that reversible self-dual codes have only been developed over field of order 2 and order 4. In this article, we construct reversible self-dual code over any finite field of order F_q , with natural number q=2. We first examine and prove some of fundamental properties of reversible self-dual code over . After a thorough analysis these, we obtain a new generator matrix of reversible self-dual code. A new generator matrix is derived from existing self-dual and reversible self-dual code over . It will be shown that a new reversible self-dual over can be constructs from one and more existing code by specific algebraic methods. Furthermore, using this construction, we determine the minimum distance of reversible self-dual code and ensuring its optimal performance in various applications.

Keywords

• finite field
• generator matrix
• minimum distance
• reversible self-dual code