With the rapid advances in the area of memory product, it has become more and more important to maintain its reliability while increasing the density and speed performance. Particularly, flash memory products have inherent difficulties in lengthening the limited lifetime due to the degradation of memory cell reliability caused by repeated read and/or write operations. To increase the benefits of high density flash memory, more advanced techniques such as multi-leveling the cell and signal processing has been adopted to the flash memory products. In this paper, arising challenges that leading engineers in semiconductor memory industries have confronted will be shared to further develop cutting-edge flash memory products.

In this paper, a new family ofM-ary sequences of periodpn-1 is proposed. The proposed family is constructed by the addition of cyclic shifts of anM-ary Sidel'nikov sequence and its reverse sequence. The number of sequences contained in this family is about (M-1)2times of their period and the maximum magnitude of their correlation values is upper bounded by 4 √(pn)+5.

In this paper, a new extending method of q-ary low correlation zone(LCZ) sequence sets is proposed, which is a generalization of binary LCZ sequence set by Kim, Jang, No, and Chung. Using this method, q-ary LCZ sequence set with parameters (N,M,L, isin) is extended as a q-ary LCZ sequence set with parameters (pN, pM, plfloor(L + 1)/plfloor - 1, pisin), where p is prime and p|q.

In this paper, we proposed a new quaternary low correlation zone(LCZ) sequence set with parameters (2(2n− 1),M, L, 2). The new LCZ sequence set is constructed from the binary sequence with ideal autocorrelation of period 2n− 1. The proposed construction method corresponds to the generalization of the construction method of binary LCZ sequence set by using binary sequence with ideal autocorrelation proposed by Kim, Jang, No, and Chung [1].

In this paper, for a positive integer M and a prime p such that M|pn- 1, a family of M-ary sequences using the M-ary Sidel'nikov sequences with period pn-1 is constructed. This family has its maximum magnitude of correlation values upper bounded by 3radic(pn) + 6 and the family size is (M-I)2(2n-1-1) + M - 1 for p = 2 or (M-1)2(pn-3)/2+ M (M-1)/2 for an odd prime p.

In this correspondence, for a positive integerMand a prime p such that M|pn- 1, three families of M-ary sequences using theM-ary Sidel'nikov sequences with period pn- 1 are constructed. Two small families contain [(pn- 1)/2]+M-2 or pn+M-3M-ary sequences, and both of their maximum magnitudes of correlation values are upper bounded by 2 radic{pn} + 6. The largest family has its maximum magnitude of correlation values upper bounded by 3 radic{pn}+5 and the family size is (M-1)2(2n-1-1) +M-1 for p = 2 or (M-1)2(pn- 3)/2 +M(M-1)/2 for an odd prime p.

In this paper, we propose the new construction methods of constructing optimal low correlation zone (LCZ) sequences. We construct the new p-ary LCZ sequence sets by adopting p-ary sequence of period pm- 1 with ideal autocorrelation for integers n and m such that m n as a column sequence. The new construction methods give us the optimal sets with respect to the bound by Tang, Fan, and Matsufuji

In this paper, we derive the cyclotomic numbers of order 5 over an extension field Fpnusing the well-known results of quintic Jacobi sums over Fp(B. C. Berndt, et al., 1998). For p ne 1 mod 5, we have obtained the simple closed-form expression of the cyclotomic numbers of order 5 over Fpn. For p equiv 1 mod 5, we express the cyclotomic number of order 5 over Fpnin terms of the solution of the diophantine system which is required to evaluate the cyclotomic number of order 5 over Fpn. Using the cyclotomic numbers of order 5 over Fpn, autocorrelation distributions of 5-ary Sidel'nikov sequences of period pn- 1 are also derived

In this paper, we derived the autocorrelation distributions, i.e., the values and the number of occurrences of each value of the autocorrelation function of Sidel'nikov sequences. The frequency of each autocorrelation value of an M-ary Sidel'nikov sequence is expressed in terms of the cyclotomic numbers of order M. It is also pointed out that the total number of distinct autocorrelation values is dependent not only on M but also on the period of the sequence, but always less than or equal to (2M) + 1

In this paper, we derive linear complexity over Fpof the M-ary Sidel'nikov sequences using discrete Fourier transform. As an example, we represent the linear complexity of the ternary Sidel'nikov sequences. It turned out that the ternary Sidel'nikov sequences have the linear complexity nearly close to their periods

For a prime p and positive integers M and n such that M|p/sup n/-1, Sidel'nikov introduced M-ary sequences (called Sidel'nikov sequences) of period p/sup n/-1, the out-of-phase autocorrelation magnitude of which is upper bounded by 4. In this correspondence, we derived the autocorrelation distributions, i.e., the values and the number of occurrences of each value of the autocorrelation function of Sidel'nikov sequences. The frequency of each autocorrelation value of an M-ary Sidel'nikov sequence is expressed in terms of the cyclotomic numbers of order M. It is also pointed out that the total number of distinct autocorrelation values is dependent not only on M but also on the period of the sequence, but always less than or equal to (M/2)+1.