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 investigates the structures and properties of one-Lee weight codes and two-Lee weight projective codes over Z4.The authors first give the Pless identities on the Lee weight of linear codes over Z_4.Then the...This paper investigates the structures and properties of one-Lee weight codes and two-Lee weight projective codes over Z4.The authors first give the Pless identities on the Lee weight of linear codes over Z_4.Then the authors study the necessary conditions for linear codes to have one-Lee weight and two-Lee projective weight respectively,the construction methods of one-Lee weight and two-Lee weight projective codes over Z4 are also given.Finally,the authors recall the weight-preserving Gray map from(Z_4~n,Lee weight)to(F_2^(2n),Hamming weight),and produce a family of binary optimal oneweight linear codes and a family of optimal binary two-weight projective linear codes,which reach the Plotkin bound and the Griesmer bound.展开更多
In this paper, the MacWilliams type identity for the m-ply Lee weight enumerator for linear codes over F2 ＋uF2 is determined. As an application of this identity, the authors obtain a MacWilliams type identity on Lee ...In this paper, the MacWilliams type identity for the m-ply Lee weight enumerator for linear codes over F2 ＋uF2 is determined. As an application of this identity, the authors obtain a MacWilliams type identity on Lee weight for linear codes over F2m ＋ uF2m. Furthermore, the authors prove a duality for the m-ply Lee weight distributions by taking advantage of the Krawtchouk polynomials.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 Nos.61202068 and 11126174Talents youth Fund of Anhui Province Universities under Grant No.2012SQRL020ZDsupported by Key Discipline Construction of Hefei University 2014XK08
文摘This paper investigates the structures and properties of one-Lee weight codes and two-Lee weight projective codes over Z4.The authors first give the Pless identities on the Lee weight of linear codes over Z_4.Then the authors study the necessary conditions for linear codes to have one-Lee weight and two-Lee projective weight respectively,the construction methods of one-Lee weight and two-Lee weight projective codes over Z4 are also given.Finally,the authors recall the weight-preserving Gray map from(Z_4~n,Lee weight)to(F_2^(2n),Hamming weight),and produce a family of binary optimal oneweight linear codes and a family of optimal binary two-weight projective linear codes,which reach the Plotkin bound and the Griesmer bound.
基金supported by National Natural Science Funds of China under Grant No.60973125College Doctoral Funds of China under Grant No.20080359003+1 种基金Anhui College Natural Science Research Project under Grant No.KJ2010B171Research Project of Hefei Normal University under Grant No.2012kj10
文摘In this paper, the MacWilliams type identity for the m-ply Lee weight enumerator for linear codes over F2 ＋uF2 is determined. As an application of this identity, the authors obtain a MacWilliams type identity on Lee weight for linear codes over F2m ＋ uF2m. Furthermore, the authors prove a duality for the m-ply Lee weight distributions by taking advantage of the Krawtchouk polynomials.
