• Journal of the Institute of Electronics Engineers of Korea TC
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• v.45 no.7
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• pp.17-21
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• 2008

As with the binary pseudo-random sequences q-ary m-sequences possess very good properties which make them useful in many applications. So we construct a class of Jacket matrices by applying additive characters of the finite field $F_q$ to entries of all shifts of q-ary m-sequence. In this paper, we generalize a method of obtaining conventional Hadamard matrices from binary PN-sequences. By this way we propose Jacket matrix construction based on q-ary M-sequences.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.10C
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• pp.959-964
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• 2007

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

• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.11C
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• pp.1059-1065
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• 2007

In this paper, we propose a class of polyphase signature sequences, whose general odd correlation properties are useful for M-ary phase signaling systems. The maximum magnitude of the general odd correlation functions of the proposed sequences are investigated and compared with those of FZC (Frank-Zadoff-Chu) sequences and those of EOE (equivalent odd and even correlation) sequences. The performance of the asynchronous M-ary phase signaling systems using the proposed sequences is simulated and compared with that using FZC sequences in direct sequence code division multiple access (DS/CDMA) systems. The performance of the system using the proposed sequence is shown to be better than that using FZC sequences when the multipath fading is in existence.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.10C
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• pp.929-934
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• 2007

In this paper, we enumerate the number of distinct autocorrelation distributions that M-ary Sidel'nikov sequences can have, while we change the primitive element for generating the sequence. Let p be a prime and $M|p^n-1$. For M=2, there is a unique autocorrelation disuibution. If M>2 and $M|p^k+1$ for some k, $1{\leq}k, then the autocorrelatin distribution of M-ary Sidel'nikov sequences is unique. If M>2 and $M{\nmid}p^k+1$ for any k, $1{\leq}k, then the autocorrelation distribution of M-ary Sidel'nikov sequences is less than or equal to ${\phi}(M)/k'(or\;{\phi}(M)/2k')$, where k' is the smallest integer satisfying $M|p^{k'}-1$.

• The Journal of the Korea institute of electronic communication sciences
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• v.7 no.4
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• pp.821-826
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• 2012

p-ary sequences of period $N=2^k-1$ are widely used in many areas of engineering and sciences. Some well-known applications include coding theory, code-division multiple-access (CDMA) communications, and stream cipher systems. The analysis of cross-correlations of these sequences is a very important problem in p-ary sequences research. In this paper, we analyze cross-correlations of p-ary sequences which is associated with the equation $(x+1)^d=x^d+1$ over finite fields.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.9C
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• pp.835-842
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• 2003

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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.31 no.12C
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• pp.1150-1156
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• 2006

In this paper we derive some lower bounds on the linear complexity and upper bounds on the 1-error linear complexity over $F_p$ of M-ary Sidel'nikov sequences of period $p^m-1$ when $M\geq3$ and $p\equiv{\pm}1$ mod M. In particular, we exactly compute the 1-error linear complexity of ternary Sidel'nikov sequences when $p^m-1$ and $m\geq4$. Based on these bounds we present the asymptotic behavior of the normalized linear complexity and the normalized 1-error linear complexity with respect to the period.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.10A
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• pp.816-829
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• 2003

In this paper, we evaluate the performance of PN (Pseudo Noise) code based time hopping sequences for M-ary UWB (Ultra Wide Band) multiple access systems using the equicorrelated signal sets. In particular, we consider two different types of M-ary UWB systems in UWB indoor wireless multipath channels: The first type of the systems (System #1) has identical symbol transmission rate regardless of the number of symbols M since the length of signal pulse train is fixed while M increases, and the second type of the systems (System #2) has the same bit transmission rate regardless of M since the length of signal pulse train is extended according to the increase of M. We compare the proposed systems with those using the ideal random time hopping sequence in terms of the symbol error rate performance. Simulation results show that the PN code based time hopping sequence achieves quite good performance which is favorably comparable to that of the ideal random sequence. Moreover, as M increases, we observe that System #2 shows better robustness against multiple access interference than System # 1.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.30 no.8C
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• pp.735-741
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• 2005

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 oかy on M but also on the sequence, but always less than or equal to ($\frac{M}{2}$)+1.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.29 no.6C
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• pp.763-769
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• 2004

It is known that a bent function corresponds to a perfect nonlinear function, which makes it difficult to do the differential cryptanalysis in DES and in many other block ciphers. In this paper, for an odd prime p, quadratic p-ary bent functions defined on finite fields are given from the families of p-ary sequences with optimal correlation properly. And quadratic p-ary bent functions, that is, perfect nonlinear functions from the finite field F $_{p^{m}}$ to its prime field $F_{p}$ are constructed by using the trace functions. trace functions.