Kyoki Imamura

A fast algorithm for determining the linear complexity of a sequence with period p/sup n/ over GF(q)

A fast algorithm is presented for determining the linear complexity of a sequence with period p/sup n/ over GF (q), where p is an odd prime, and where q is a prime and a primitive root (mod p/sup 2/).

An algorithm for the k -error linear complexity of sequences over GF ( p m ) with period p n , p a prime

An algorithm is given for the k-error linear complexity of sequences over GF(pm) with period pn, p a prime. The algorithm is derived by the generalized Games?Chan algorithm for the linear complexity of sequences over GF(pm) with period pn and by using the modified cost different from that used in the Stamp?Martin algorithm for sequences over GF(2) with period 2n. A method is also given for computing an error vector which gives the k-error linear complexity.

Balanced nonbinary sequences with good periodic correlation properties obtained from modified Kumar-Moreno sequences

Kumar and Moreno (see ibid., vol.37, no.3, p.603, 1991) presented a new family of nonbinary sequences which has not only good periodic correlation properties but also the largest family size. First, the unbalanced properties for Kumar-Moreno sequences are pointed out. Second, a new family of balanced nonbinary sequences obtained from modified Kumar-Moreno sequences is proposed, and it is shown that the new family has the same optimal periodic nontrivial correlation as the family of Kumar-Moreno sequences and consists of the balanced nonbinary sequences. It is also shown that the cost of making sequences balanced is a decrease of the family size in addition to the condition that n is an even number. In particular, let the length of Kumar-Moreno sequences and the new sequences be the same and equal to p/sup n/-1 with n even, then the family size of the new sequences is p/sup n/2/ which is much smaller than p/sup n/, that of Kumar-Moreno sequences. >

Linear complexity of a sequence obtained from a periodic sequence by either substituting, inserting, or deleting k symbols within one period

A unified derivation of the bounds of the linear complexity is given for a sequence obtained from a periodic sequence over GF(q) by either substituting, inserting, or deleting k symbols within one period. The lower bounds are useful in case of n<N/k, where N and n are the period and the linear complexity of the sequence, respectively. It is shown that all three different cases can be treated very simply in a unified manner. The bounds are useful enough to show how wide the distribution of the linear complexity becomes as k increases, although they are not always tight because their derivations do not use the information about the change values.

A New Algorithm for the k -Error Linear Complexity of Sequences over GF(pm) with Period pn

A new algorithm is given for the k-error linear complexity of sequences over GF (p m) with period p n, p a prime. The algorithm is different from the previous one recently given by the authors in the following two points and can be regarded as generalization of the Stamp-Martin algorithm for the k -LC of binary sequences with period 2n. First the value of k decreases at each iteration. Secondly the error vector for the k -LC can be determined at the same time when the k -LC is obtained. The key ideas of the algorithm are “shift” and “offset” of the cost matrix which are introduced by the authors to derive the Stamp-Martin algorithm for binary sequences from our previous algorithm.

A method for computing addition tables in GF(p^n) (Corresp.)

Conway showed that a table of Zechs logarithms is useful to perform addition in GF (p^{n}) when the elements are represented as powers of a primitive element. The Zechs logarithm Z(x) of x is defined by the equation \alpha^{z(x)}=\alpha^{x} + 1 , where \alpha is a primitive element, zero is written as \alpha^{\ast} , and x=\ast,O,1, \cdots ,p^{n}-2 . A simple algorithm for making a table of Zechs logarithms is presented.

Linear complexity for one-symbol substitution of a periodic sequence over GF(q)

It is shown that the linear complexity for one-symbol substitution of any periodic sequence over GF(q) can be computed without any condition on the minimal polynomial of the sequence.

Real-Valued Bent Function and Its Application to the Design of Balanced Quadriphase Sequences with Optimal Correlation Properties

A real-valued bent function is newly defined and shown to be useful to design polyphase sequences with optimal correlation properties. As an application of practical importance, balanced quadriphase sequences with optimal correlation properties are designed and shown to be the sum of two binary {1,−1} bent sequences.

Balanced quadriphase sequences with optimal periodic correlation properties constructed by real-valued bent functions

The real-valued bent function was previously introduced by the authors (1991) as a generalization of the usual p-ary bent function, p a prime, in such a way that the range of the function is the set of real numbers, i.e. not restricted to GF(p). The real-valued bent function was used to construct a family of 2/sup n/2/ balanced quadriphase sequences of period 2/sup n/-1 with optimal periodic correlation properties, where n is a multiple of four. A class of real-valued bent functions that map the set of all the m-tuples over GF(2) into the set (0,1/2,1,3/2) for an arbitrary m is given. This is applied to generalize a previous construction to the case where n is even, i.e. not restricted to a multiple of four. It is also shown that the quadriphase sequences given by T. Novosad can be considered as one kind of sequence constructed by real-valued bent functions. Conditions are given for some families of the quadriphase sequences constructed by some real-valued bent functions to be balanced. The exact distributions of the periodic correlation values are derived for the families of the balanced quadriphase sequences. >

Asymptotic behavior of normalized linear complexity of ultimately nonperiodic binary sequences

This paper describes the asymptotic behavior of normalized linear complexity of ultimately nonperiodic binary sequence. The linear complexity of s/sup n/, L/sub s/(n), is defined as the length of the shortest linear feedback shift register which generates s/sup n/. The research method and results studied in this paper seem to be very useful in characterizing the purely random sequence and distinguishing a key stream generator from a uniformly random sequence.