This paper discusses the enumeration of 1-generator quasi-cyclic codes and describes an algorithm which will obtain one, and only one, generator for each 1-generator quasi-cyclic code.
We focus on the L^(p)(R^(2))theory of the fractional Fourier transform(FRFT)for 1≤p≤2.In L^(1)(R^(2)),we mainly study the properties of the FRFT via introducing the two-parameter chirp operator.In order to get the p...We focus on the L^(p)(R^(2))theory of the fractional Fourier transform(FRFT)for 1≤p≤2.In L^(1)(R^(2)),we mainly study the properties of the FRFT via introducing the two-parameter chirp operator.In order to get the pointwise convergence for the inverse FRFT,we introduce the fractional convolution and establish the corresponding approximate identities.Then the well-defined inverse FRFT is given via approximation by suitable means,such as fractional Gauss means and Able means.Furthermore,if the signal F_(α,β)f is received,we give the process of recovering the original signal f with MATLAB.In L^(2)(R^(2)),the general Plancherel theorem,direct sum decomposition,and the general Heisenberg inequality for the FRFT are obtained.展开更多
基金The research is supported by the Tian Yuan Foundation under Grant No. K1107320 and the National Natural Science Foundation of China under Grant No, K1107645,Acknowledgement The authors wish to thank their supervisor Dr. Jie Cui for suggesting several corrections which improved the final manuscript.
文摘This paper discusses the enumeration of 1-generator quasi-cyclic codes and describes an algorithm which will obtain one, and only one, generator for each 1-generator quasi-cyclic code.
基金supported by the National Natural Science Foundation of China(Grant No.11601427)the China Postdoctoral Science Foundation(No.2017M613193)the Natural Science Basic Research Plan in Shaanxi Province of China(No.2017JQ1009).
文摘We focus on the L^(p)(R^(2))theory of the fractional Fourier transform(FRFT)for 1≤p≤2.In L^(1)(R^(2)),we mainly study the properties of the FRFT via introducing the two-parameter chirp operator.In order to get the pointwise convergence for the inverse FRFT,we introduce the fractional convolution and establish the corresponding approximate identities.Then the well-defined inverse FRFT is given via approximation by suitable means,such as fractional Gauss means and Able means.Furthermore,if the signal F_(α,β)f is received,we give the process of recovering the original signal f with MATLAB.In L^(2)(R^(2)),the general Plancherel theorem,direct sum decomposition,and the general Heisenberg inequality for the FRFT are obtained.
