This paper firstly gives some necessary conditions on one-Gray weight linear codes. And then we use these results to construct several classes of one-Gray weight linear codes over Z_4 +uZ_4(u^2=u) with type 16^(k_1)8^...This paper firstly gives some necessary conditions on one-Gray weight linear codes. And then we use these results to construct several classes of one-Gray weight linear codes over Z_4 +uZ_4(u^2=u) with type 16^(k_1)8^(k_2)8^(k_3)4^(k_4)4^(k_5)4^(k_6)2^(k_7)2^(k_8) based on a distance-preserving Gray map from(Z4 + u Z4)n to Z2n4. Secondly, the authors use the similar approach to do works on two-Gray(projective) weight linear codes. Finally, some examples are given to illustrate the construction methods.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.61672036 and 61202068the Open Research Fund of National Mobile Communications Research Laboratory,Southeast University under Grant No.2015D11+1 种基金Technology Foundation for Selected Overseas Chinese Scholar,Ministry of Personnel of China under Grant No.05015133Key projects of support program for outstanding young talents in Colleges and Universities under Grant No.gxyq ZD2016008
文摘This paper firstly gives some necessary conditions on one-Gray weight linear codes. And then we use these results to construct several classes of one-Gray weight linear codes over Z_4 +uZ_4(u^2=u) with type 16^(k_1)8^(k_2)8^(k_3)4^(k_4)4^(k_5)4^(k_6)2^(k_7)2^(k_8) based on a distance-preserving Gray map from(Z4 + u Z4)n to Z2n4. Secondly, the authors use the similar approach to do works on two-Gray(projective) weight linear codes. Finally, some examples are given to illustrate the construction methods.
