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Sang-Hyo Kim,Jong-Seon No,Habong Chung,Helleseth, T. IEEE 2005 IEEE transactions on information theory Vol.51 No.3
<P>For a prime power q, we show that a cyclic relative difference set with parameters (q/sup n/-1/q-1,q-1,q/sup n-1/,q/sup n-2/) can be constructed from a d-homogeneous function from F/sub q//sup n//spl bsol/{0} onto F/sub q/ with difference-balanced property, where F/sub q//sup n/ is the finite field with q/sup n/ elements. This construction method enables us to construct several new cyclic relative difference sets with parameters (p/sup n/-1/p/sup l/-1,p/sup l/-1,p/sup n-l/,p/sup n-2l/) from p-ary sequences of period p/sup n/-1 with ideal autocorrelation property introduced by Helleseth and Gong. Using a lifting idea, other new cyclic relative difference sets can be constructed from the Helleseth-Gong (HG) sequences. Also, the 3-ranks and the trace representation of the characteristic sequences of cyclic relative difference sets from a specific class of ternary HG sequences and ternary Lin sequences are derived.</P>
최적의 상관 특성과 큰 선형 복잡도를 갖는 새로운 p-진 수열군
장지용,김영식,노종선,Tor Helleseth 한국통신학회 2003 韓國通信學會論文誌 Vol.28 No.9C
For an odd prime p and integer n, m and k such that n=(2m+1)ㆍk, a new family of p-ary sequences of period p$^{n}$ -1 with optimal correlation property is constructed using the p-ary Helleseth-Gong sequences with ideal autocorrelation, where the size of the sequence family is p$^{n}$ . That is, the maximum nontrivial correlation value R$_{max}$ of all pairs of distinct sequences in the family does not exceed p$^{n}$ 2/ +1, which means the optimal correlation property in terms of Welch's lower bound. It is also derived that the linear span of the sequences in the family is (m+2)ㆍn except for the m-sequence in the family.
New family of p-ary sequences with optimal correlation property and large linear span
Jang, J.-W.,Kim, Young-Sik,No, Jong-Seon,Helleseth, T. IEEE 2004 IEEE transactions on information theory Vol.50 No.8
For an odd prime p and integers n, m, and k such that n=(2m+1)k, a new family of p-ary sequences of period p<SUP>n</SUP>-1 with optimal correlation property is constructed using the p-ary Helleseth-Gong sequences with ideal autocorrelation, where the size of the sequence family is p<SUP>n</SUP>. That is, the maximum nontrivial correlation value R<SUB>max</SUB> of all pairs of distinct sequences in the family does not exceed p<SUP>n</SUP>2/+1, which means the family has optimal correlation in terms of Welch's lower bound. The symbol distribution of the sequences in the family is enumerated. It is also shown that the linear span of the sequences in the family is (m+2)n except for the m-sequence in the family.
Seokbeom Hong,Hosung Park,Jong-Seon No,Helleseth, Tor,Young-Sik Kim IEEE 2014 IEEE transactions on information theory Vol.60 No.6
<P>In this paper, a new class of (N, K) near-optimal partial Hadamard codebooks is proposed. The construction of the proposed codebooks from Hadamard matrices is based on binary row selection sequences, which are generated by quadratic have parameters N = p<SUP>n</SUP> and K = (p - 1/2 p)(N + √N) + 1 for an odd prime p and an even positive integer n. We prove that the maximum magnitude of inner products between the code vectors of the proposed codebooks asymptotically achieves the Welch bound equality for sufficiently large p and derive their inner product distribution.</P>