伽罗瓦内积是欧式内积和厄尔米特内积的推广, 常循环码是一类结构丰富而又应用广泛的线性码, MDS码被著名学者MacWilliams和Sloane称为最富有魅力的纠错码, LCD码被广泛的应用于数据存储, 通信系统, 电子和密码学等. 文章将研究基于伽罗瓦内积下的LCD常循环码和LCD MDS码, 重点讨论了有限域上常循环码的伽罗瓦对偶码的形式及伽罗瓦LCD常循环码的充要条件, 并得到了三类特殊参数的伽罗瓦LCD MDS码.

Galois inner product is an extension of Euclidean inner product and Hermitian inner product. Constacyclic codes are a class of linear codes, which have a rich algebraic structure and wide appplication. MDS codes have been described by renowned scholars MacWilliams and Sloane as the most enchanting error-correcting codes. LCD codes are widely used in datastorage, communication systems, electronics and cryptopraphy. In this paper, we study the LCD constacyclic codes and LCD MDS codes based on the Galois inner product. We mainly discuss the usual form of Galois dual constacyclic codes and the necessary and sufficient conditions of Galois LCD constacyclic codes in finite fields, and obtain three types of special Galois LCD MDS codes.