| Let Fq be a finite field with q=pe elements,where p is a prime and e is a positive integer.In 2017,Fan and Zhang introduced l-Galois inner products on the n-dimensional vector space Fqn,where 0?l<e.l-Galois inner products are a generalization of the Euclidean inner product(when l=0)and the Hermitian inner product(when e is even and l=e/2),which enriches algebraic structures of linear codes.l-Galois self-orthogonal codes are a generalization of Euclidean self-orthogonal codes and Hermitian self-orthogonal codes,which can be used to con-struct entanglement-assisted quantum error-correcting codes.So far,there are many researches on Euclidean self-orthogonal codes and Hermitian self-orthogonal codes,but few on general l-Galois self-orthogonal codes.Constacyclic codes have excellent algebraic properties,and it is a meaningful subject to study the self-orthogonality of constacyclic codes under l-Galois inner products.In this paper,we study l-Galois self-orthogonal A-constacyclic codes of length n over the finite field Fq,where q=pe,p is prime,e is a positive integer,n is coprime to q,??Fq*and 0?l<e.We obtain the following results:Firstly,a sufficient and necessary condition for the existence of nonzero l-Galois self-orthogonal ?-constacyclic codes of length n over Fq is given,and sufficient and necessary conditions for ?-constacyclic codes of length n over Fq being l-Galois self-orthogonal codes are also found.Secondly,formula to enumerate the number of l-Galois self-orthogonal A-constacyclic codes of length n over Fq is presented.Based on this,dimensions of l-Galois self-orthogonal ?-constacyclic codes of length n over Fq are given,and formula to enumerate the number of l-Galois self-orthogonal?-constacyclic codes of length n and dimension k over Fq is found.In particular,formula to enumerate the number of l-Galois self-dual ?-constacyclic codes of length n over Fq is obtained.Finally,a family of l-Galois self-orthogonal ?-constacyclic MDS codes over Fq is constructed. |
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