Existence And Properties Of Complementary-dual Codes Of Skew ?-cyclic Codes Over Finite Fields

Cyclic codes have efficient coding and decoding algorithms,which have an extremely important position in error correction code theory,and are most commonly used in the field of communication.The construction of cyclic codes is generally through polynomial rings and ideals.On the basis of the ordinary polynomial ring,an automorphism map is introduced to obtain the skew polynomial ring.The joining of automorphism mapping makes the skew polynomial ring non-exchangeable.This non-commutability makes the code words on the oblique polynomial ring have more discussion space.Then we can generalize cyclic codes to skew cyclic codes.As a kind of special linear codes,linear complementary dual code(LCD code)has a wide range of applications in error correction code theory.Linear complementary dual codes have good correlation properties and orthogonal properties Domestic and foreign scholars have done a lot of research on the existence,structure,weight distribution,optimal code and its application in the isochronous code of linear complementary dual code.In this paper,the linear complementary dual code is extended to the skew ?-cyclic codes over finite fields.Based on the linear space theory,the necessary and suff-icient conditions for its existence and related properties of the linear complementary dual codes in the skew ?-cyclic codes over finite fields are discussed.In this paper,a new polynomial ring is obtained by introducing automorphism mapping and polynomial theory over finite fields.The skew ?-cyclic codes are redefined and their properties and new multiplication operations are studied.We use the polynomial theory over the finite field,through the generator polynomial of the code,the generator matrix,etc.,discuss the necessary and sufficient conditions of the linear complementary dual codes in the skew ?-cyclic codes,and discuss the minimum distance problem of the linear complementary dual code.By the theory of circular circle coset,we also discuss the counting problem of some LCD codes,when the ? =-1 in the A-Cyclic Codes,we study the count of the MDS negative cycle LCD code when satisfied q?1mod2n,and the count of the MDS negative cycle LCD code when satisfied q?-1mod 2n,and the counting of the LCD code in two special cases in the Skew ?-Cyclic Codes.