This paper presents an algorithm for blind recognition of punctured convo-lutional codes which is an important problem in adaptive modulation and coding. For a given finite sequence of convolutional code, the parity c...This paper presents an algorithm for blind recognition of punctured convo-lutional codes which is an important problem in adaptive modulation and coding. For a given finite sequence of convolutional code, the parity check matrix of the convolutional code is first computed by solving a linear system with adequate error tolerance. Then a minimal basic encoding matrix of the original convolutional code and its puncturing pattern are determined according to the known parity check matrix of the punctured convolutional code.展开更多
In this paper, a statistical recognition method of the binary BCH code is proposed. The method is applied to both primitive and non-primitive binary BCH code. The block length is first recognized based on the cyclic f...In this paper, a statistical recognition method of the binary BCH code is proposed. The method is applied to both primitive and non-primitive binary BCH code. The block length is first recognized based on the cyclic feature under the condition of the frame length known. And then candidate polynomials are achieved which meet the restrictions. Among the candidate polynomials, the most optimal polynomial is selected based on the minimum rule of the weights sum of the syndromes. Finally, the best polynomial was factorized to get the generator polynomial recognized. Simulation results show that the method has strong capability of anti-random bit error. Besides, the algorithm proposed is very simple, so it is very practical for hardware im-plementation.展开更多
This paper studies （1 ＋ u）-constacyelic codes over the ring F2 ＋ uF2 ＋ vF,2 ＋ uvF2. It is proved that the image of a （1 ＋ u）-constacyclic code of length n over F2 ＋ uF2 ＋ vF2 ＋uvF2 under a Gray map is a di...This paper studies （1 ＋ u）-constacyelic codes over the ring F2 ＋ uF2 ＋ vF,2 ＋ uvF2. It is proved that the image of a （1 ＋ u）-constacyclic code of length n over F2 ＋ uF2 ＋ vF2 ＋uvF2 under a Gray map is a distance invariant binary quasi-cyclic code of index 2 and length 4n. A set of generators of such constacyclic codes for an arbitrary length is determined, Some optimal binary codes are obtained directly from （1 ＋ u）-constacyclic codes over F2 ＋ uF2 ＋ vF2 ＋ uvF2.展开更多
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 introduces a Gray map from （Fp ＋ vFp）n to F2pn, and describes the relationship between codes over Fp ＋ vFp and their Gray images. The authors prove that every cyclic code of arbitrary length n over Fp ...This paper introduces a Gray map from （Fp ＋ vFp）n to F2pn, and describes the relationship between codes over Fp ＋ vFp and their Gray images. The authors prove that every cyclic code of arbitrary length n over Fp ＋ vFp is principal, and determine its generator polynomial as well as the number of cyclic codes. Moreover, the authors obtain many best-known p-ary quasic-cyclic codes in terms of their parameters via the Gray map.展开更多
基金the National Namral Science Foundation of China(Grant Nos.10171017,90204013)Special Funds ofAuthorsofExcellentDoctoralDissertationinChina(GrantNo.200084) Shanghai Science and Technology Funds(Grant No.0351 1501)
文摘This paper presents an algorithm for blind recognition of punctured convo-lutional codes which is an important problem in adaptive modulation and coding. For a given finite sequence of convolutional code, the parity check matrix of the convolutional code is first computed by solving a linear system with adequate error tolerance. Then a minimal basic encoding matrix of the original convolutional code and its puncturing pattern are determined according to the known parity check matrix of the punctured convolutional code.
文摘In this paper, a statistical recognition method of the binary BCH code is proposed. The method is applied to both primitive and non-primitive binary BCH code. The block length is first recognized based on the cyclic feature under the condition of the frame length known. And then candidate polynomials are achieved which meet the restrictions. Among the candidate polynomials, the most optimal polynomial is selected based on the minimum rule of the weights sum of the syndromes. Finally, the best polynomial was factorized to get the generator polynomial recognized. Simulation results show that the method has strong capability of anti-random bit error. Besides, the algorithm proposed is very simple, so it is very practical for hardware im-plementation.
基金supported by the National Natural Science Foundation of China under Grant No.60973125the Natural Science Foundation of Anhui Province under Grant No.1208085MA14the Fundamental Research Funds for the Central Universities under Grants Nos.2012HGXJ0040 and 2011HGBZ1298
文摘This paper studies （1 ＋ u）-constacyelic codes over the ring F2 ＋ uF2 ＋ vF,2 ＋ uvF2. It is proved that the image of a （1 ＋ u）-constacyclic code of length n over F2 ＋ uF2 ＋ vF2 ＋uvF2 under a Gray map is a distance invariant binary quasi-cyclic code of index 2 and length 4n. A set of generators of such constacyclic codes for an arbitrary length is determined, Some optimal binary codes are obtained directly from （1 ＋ u）-constacyclic codes over F2 ＋ uF2 ＋ vF2 ＋ uvF2.
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 NNSF of China under Grant Nos.11126174,60973125,71071045 and 71001032Talents youth Fund of Anhui Province Universities under Grant No.2012SQRL020ZD+1 种基金Youth Science Research Fund of Anhui University under Grant No.2009QN026Bthe 211 Project of Anhui University Grant No. KJTD002B
文摘This paper introduces a Gray map from （Fp ＋ vFp）n to F2pn, and describes the relationship between codes over Fp ＋ vFp and their Gray images. The authors prove that every cyclic code of arbitrary length n over Fp ＋ vFp is principal, and determine its generator polynomial as well as the number of cyclic codes. Moreover, the authors obtain many best-known p-ary quasic-cyclic codes in terms of their parameters via the Gray map.
