This paper is devoted to the construction of one-Lee weight codes and two-Lee weight codes over IF_p+vIF_p(v^2=v) with type p^(2 k_1)p^(k2)p^(k3) based on two different distance-preserving Gray maps from((IF_p+vIF_p)~...This paper is devoted to the construction of one-Lee weight codes and two-Lee weight codes over IF_p+vIF_p(v^2=v) with type p^(2 k_1)p^(k2)p^(k3) based on two different distance-preserving Gray maps from((IF_p+vIF_p)~n, Lee weight) to(IF_p^(2 n), Hamming weight), where p is a prime. Moreover, the authors prove that the obtained two-Lee weight codes are projective only when p=2.展开更多
This paper is devoted to determining the structures and properties of one-Lee weight codes and two-Lee weight projective codes Ck1,k2,k3 over p IF+ v IFp with type p2k1pk2pk3. The authors introduce a distance-preservi...This paper is devoted to determining the structures and properties of one-Lee weight codes and two-Lee weight projective codes Ck1,k2,k3 over p IF+ v IFp with type p2k1pk2pk3. The authors introduce a distance-preserving Gray map from( IFp + v IFp)nto2np. By the Gray map, the authors construct a family of optimal one-Hamming weight p-ary linear codes from one-Lee weight codes over IFp+ v IFp, which attain the Plotkin bound and the Griesmer bound. The authors also obtain a class of optimal p-ary linear codes from two-Lee weight projective codes over IFp + vIFp, which meet the Griesmer bound.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.61202068Technology Foundation for Selected Overseas Chinese Scholar,Ministry of Personnel of China under Grant No.05015133+1 种基金the Open Research Fund of National Mobile Communications Research Laboratory,Southeast University under Grant No.2015D11Key Projects of Support Program for Outstanding Young Talents in Colleges and Universities under Grant No.gxyqZD2016008
文摘This paper is devoted to the construction of one-Lee weight codes and two-Lee weight codes over IF_p+vIF_p(v^2=v) with type p^(2 k_1)p^(k2)p^(k3) based on two different distance-preserving Gray maps from((IF_p+vIF_p)~n, Lee weight) to(IF_p^(2 n), Hamming weight), where p is a prime. Moreover, the authors prove that the obtained two-Lee weight codes are projective only when p=2.
基金supported by the National Natural Science Foundation of China under Grant No.61202068Talented youth Fund of Anhui Province Universities under Grant No.2012SQRL020ZDthe Technology Foundation for Selected Overseas Chinese Scholar,Ministry of Personnel of China under Grant No.05015133
文摘This paper is devoted to determining the structures and properties of one-Lee weight codes and two-Lee weight projective codes Ck1,k2,k3 over p IF+ v IFp with type p2k1pk2pk3. The authors introduce a distance-preserving Gray map from( IFp + v IFp)nto2np. By the Gray map, the authors construct a family of optimal one-Hamming weight p-ary linear codes from one-Lee weight codes over IFp+ v IFp, which attain the Plotkin bound and the Griesmer bound. The authors also obtain a class of optimal p-ary linear codes from two-Lee weight projective codes over IFp + vIFp, which meet the Griesmer bound.
