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
Projective Reed-Solomon code is an important class of maximal distance separable codes in reliable communication and deep holes play important roles in its decoding.In this paper,we obtain two classes of deep holes of...Projective Reed-Solomon code is an important class of maximal distance separable codes in reliable communication and deep holes play important roles in its decoding.In this paper,we obtain two classes of deep holes of projective Reed-Solomon codes over finite fields with even characteristic.That is,let F_(q) be finite field with even characteristic,k∈{2,q-2},and let u(x)be the Lagrange interpolation polynomial of the first q components of the received vector u∈F_(q)+1 q Suppose that the(q+1)-th component of u is 0,and u(x)=λx^(k)+f_(≤k-2)(x),λx^(q-2)+f_(≤k-2)(x),where λ∈F^(*)_(q) and f_(≤k-2)(x)is a polynomial over F_(q) with degree no more than k-2.Then the received vector u is a deep hole of projective Reed-Solomon codes PRS(F_(q),k).In fact,our result partially solved an open problem on deep holes of projective Reed-Solomon codes proposed by Wan in 2020.展开更多
The codes of formal power series rings R_∞=F[[r]]={sum from i=0 to ∞(a_lr^l|a_l∈F)}and finite chain rings R_i={a_0+a_1r+…+a_(i-1)r^(i-1)|a_i∈F}have close relationship in lifts and projection.In this paper,we stud...The codes of formal power series rings R_∞=F[[r]]={sum from i=0 to ∞(a_lr^l|a_l∈F)}and finite chain rings R_i={a_0+a_1r+…+a_(i-1)r^(i-1)|a_i∈F}have close relationship in lifts and projection.In this paper,we study self-dual codes over R_∞by means of self-dual codes over Ri,and give some characterizations of self-dual codes over R_∞.展开更多
This paper investigates rate adaptation schemes for decoding-and-forward (DF) relay system based on random projections codes (RPC). We consider a classic three node relay system model, where relay node performs on hal...This paper investigates rate adaptation schemes for decoding-and-forward (DF) relay system based on random projections codes (RPC). We consider a classic three node relay system model, where relay node performs on half-duplex mode. Then, we give out receiving diversity relay scheme and coding diversity relay scheme, and present their jointly decoding methods. Furthermore, we discuss the performance of the two schemes with different power allocation coefficients. Simulations show that our relay schemes can achieve different gain with the help of relay node. And, we should allocate power to source node to just guarantee relay node can decode successfully, and allocate remain power to relay node as far as possible. In this way, this DF relay system not only achieves diversity gain, but also achieves higher and smooth spectrum efficiency.展开更多
The most popular and representative classic waveform codes are referred to as orthogonal,bi-orthogonal,simplex,and etc,but the choice of waveform codes is essentially identical in error performance and cross correlati...The most popular and representative classic waveform codes are referred to as orthogonal,bi-orthogonal,simplex,and etc,but the choice of waveform codes is essentially identical in error performance and cross correlation characteristic.Though bi-orthogonal coding requires half the bandwidth of the others,such coding scheme is attractive only when large bandwidth is available.In this paper,a novel finite projective plane（FPP） based waveform coding scheme is proposed,which is with similar error performance and cross correlation.Nevertheless,the bandwidth requirement will grow in a quadratic way,but not in an exponential way with the values of message bit numbers（k）.The proposed scheme takes obvious advantages over the bi-orthogonal scheme when k ≥ 6.展开更多
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 Foundation of Sichuan Tourism University(20SCTUTY01)Initial Scientific Research Fund of Doctors in Sichuan Tourism University。
文摘Projective Reed-Solomon code is an important class of maximal distance separable codes in reliable communication and deep holes play important roles in its decoding.In this paper,we obtain two classes of deep holes of projective Reed-Solomon codes over finite fields with even characteristic.That is,let F_(q) be finite field with even characteristic,k∈{2,q-2},and let u(x)be the Lagrange interpolation polynomial of the first q components of the received vector u∈F_(q)+1 q Suppose that the(q+1)-th component of u is 0,and u(x)=λx^(k)+f_(≤k-2)(x),λx^(q-2)+f_(≤k-2)(x),where λ∈F^(*)_(q) and f_(≤k-2)(x)is a polynomial over F_(q) with degree no more than k-2.Then the received vector u is a deep hole of projective Reed-Solomon codes PRS(F_(q),k).In fact,our result partially solved an open problem on deep holes of projective Reed-Solomon codes proposed by Wan in 2020.
基金Foundation item： Supported by the Scientific Research Foundation of Hubei Provincial Education Depart- ment（B2013069） Supported by the National Science Foundation of Hubei Polytechnic University（12xjzl4A, 11yjz37B）
文摘The codes of formal power series rings R_∞=F[[r]]={sum from i=0 to ∞(a_lr^l|a_l∈F)}and finite chain rings R_i={a_0+a_1r+…+a_(i-1)r^(i-1)|a_i∈F}have close relationship in lifts and projection.In this paper,we study self-dual codes over R_∞by means of self-dual codes over Ri,and give some characterizations of self-dual codes over R_∞.
文摘This paper investigates rate adaptation schemes for decoding-and-forward (DF) relay system based on random projections codes (RPC). We consider a classic three node relay system model, where relay node performs on half-duplex mode. Then, we give out receiving diversity relay scheme and coding diversity relay scheme, and present their jointly decoding methods. Furthermore, we discuss the performance of the two schemes with different power allocation coefficients. Simulations show that our relay schemes can achieve different gain with the help of relay node. And, we should allocate power to source node to just guarantee relay node can decode successfully, and allocate remain power to relay node as far as possible. In this way, this DF relay system not only achieves diversity gain, but also achieves higher and smooth spectrum efficiency.
基金supported by MOST under Grant MOST 103-2633-E-242-002
文摘The most popular and representative classic waveform codes are referred to as orthogonal,bi-orthogonal,simplex,and etc,but the choice of waveform codes is essentially identical in error performance and cross correlation characteristic.Though bi-orthogonal coding requires half the bandwidth of the others,such coding scheme is attractive only when large bandwidth is available.In this paper,a novel finite projective plane（FPP） based waveform coding scheme is proposed,which is with similar error performance and cross correlation.Nevertheless,the bandwidth requirement will grow in a quadratic way,but not in an exponential way with the values of message bit numbers（k）.The proposed scheme takes obvious advantages over the bi-orthogonal scheme when k ≥ 6.
