An A^3-code is extension of A^2-code in which none of the three participants： transmitter, receiver and arbiter, is assumed trusted. In this article, from projective geometry over finite fields, two A^3 -codes were g...An A^3-code is extension of A^2-code in which none of the three participants： transmitter, receiver and arbiter, is assumed trusted. In this article, from projective geometry over finite fields, two A^3 -codes were given, the parameters, and probabilities of successful attacks were computed.展开更多
Optical orthogonal code is the main signature code employed by optical CDMA system. Starting from modern mathematics theory, finite projective geometry and Galois theory, the essential connection between optical ortho...Optical orthogonal code is the main signature code employed by optical CDMA system. Starting from modern mathematics theory, finite projective geometry and Galois theory, the essential connection between optical orthogonal code designing and finite geometry theory were discussed; find out the corresponding relationship between the parameter of OOC and that of finite geometry space. In this article, the systematic theory of OOC designing based on projective geometry is established in detail. The designing process and results of OOC on projective plane PG(2,q) and on m-dimension projective space are given respectively. Furthermore, the analytical theory for the corresponding relation between OOC with high cross-correlation and k-D manifold of projective space is set up. The OOC designing results given in this article have excellent performance, whose maximum cross-correlation is 1, and the cardinality reaches the Johnson upper bound, i.e. it realizes the optimization in both MUI and system capacity.展开更多
Mixed orthogonal arrays of strength two and size smn are constructed by grouping points in the finite projective geometry PG(mn-1, s). PG(mn-1, s) can be partitioned into [(smn-1)/(sn-1)](n-1)-flats such that each (n-...Mixed orthogonal arrays of strength two and size smn are constructed by grouping points in the finite projective geometry PG(mn-1, s). PG(mn-1, s) can be partitioned into [(smn-1)/(sn-1)](n-1)-flats such that each (n-1)-flat is associated with a point in PG(m-1, sn). An orthogonal array Lsmn((sn)(smn-)(sn-1) can be constructed by using (smn-1)/( sn-1) points in PG(m-1, sn). A set of (st-1)/(s-1) points in PG(m-1, sn) is called a (t-1)-flat over GF(s) if it is isomorphic to PG(t-1, s). If there exists a (t-1)-flat over GF(s) in PG(m-1, sn), then we can replace the corresponding [(st-1)/(s-1)] sn-level columns in Lsmn((sn)(smn-)(sn-1) by (smn-1)/( sn-1) st -level columns and obtain a mixed orthogonal array. Many new mixed orthogonal arrays can be obtained by this procedure. In this paper, we study methods for finding disjoint (t-1)-flats over GF(s) in PG(m-1, sn) in order to construct more mixed orthogonal arrays of strength two. In particular, if m and n are relatively prime then we can construct an Lsmn((sm)smn-1/sm-1-i(sn-1)/ (s-1)( sn) i(sm-1)/ s-1) for any 0i(smn-1)(s-1)/( sm-1)( sn-1) New orthogonal arrays of sizes 256, 512, and 1024 are obtained by using PG(7,2), PG(8,2), and PG(9,2) respectively.展开更多
文摘An A^3-code is extension of A^2-code in which none of the three participants： transmitter, receiver and arbiter, is assumed trusted. In this article, from projective geometry over finite fields, two A^3 -codes were given, the parameters, and probabilities of successful attacks were computed.
基金The National Natural Science Foundationof China (No.:60272048) Natural Science Foundationof JiangsuEducation Department(No.04kjb510057) China Scholarship Council
文摘Optical orthogonal code is the main signature code employed by optical CDMA system. Starting from modern mathematics theory, finite projective geometry and Galois theory, the essential connection between optical orthogonal code designing and finite geometry theory were discussed; find out the corresponding relationship between the parameter of OOC and that of finite geometry space. In this article, the systematic theory of OOC designing based on projective geometry is established in detail. The designing process and results of OOC on projective plane PG(2,q) and on m-dimension projective space are given respectively. Furthermore, the analytical theory for the corresponding relation between OOC with high cross-correlation and k-D manifold of projective space is set up. The OOC designing results given in this article have excellent performance, whose maximum cross-correlation is 1, and the cardinality reaches the Johnson upper bound, i.e. it realizes the optimization in both MUI and system capacity.
文摘Mixed orthogonal arrays of strength two and size smn are constructed by grouping points in the finite projective geometry PG(mn-1, s). PG(mn-1, s) can be partitioned into [(smn-1)/(sn-1)](n-1)-flats such that each (n-1)-flat is associated with a point in PG(m-1, sn). An orthogonal array Lsmn((sn)(smn-)(sn-1) can be constructed by using (smn-1)/( sn-1) points in PG(m-1, sn). A set of (st-1)/(s-1) points in PG(m-1, sn) is called a (t-1)-flat over GF(s) if it is isomorphic to PG(t-1, s). If there exists a (t-1)-flat over GF(s) in PG(m-1, sn), then we can replace the corresponding [(st-1)/(s-1)] sn-level columns in Lsmn((sn)(smn-)(sn-1) by (smn-1)/( sn-1) st -level columns and obtain a mixed orthogonal array. Many new mixed orthogonal arrays can be obtained by this procedure. In this paper, we study methods for finding disjoint (t-1)-flats over GF(s) in PG(m-1, sn) in order to construct more mixed orthogonal arrays of strength two. In particular, if m and n are relatively prime then we can construct an Lsmn((sm)smn-1/sm-1-i(sn-1)/ (s-1)( sn) i(sm-1)/ s-1) for any 0i(smn-1)(s-1)/( sm-1)( sn-1) New orthogonal arrays of sizes 256, 512, and 1024 are obtained by using PG(7,2), PG(8,2), and PG(9,2) respectively.
