Takayasu Kaida

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.

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.

On Boston bound for cyclic codes by DFT with unknown elements

The Boston bound is defined by the subset of defining set for cyclic codes. The authors proposed new simple derivation for the BCH bound, the HT bound and the shift bound, using the discrete Fourier transform (DFT) and the Blahut theorem. In this paper, we consider the Boston bound for cyclic codes by the DFT.The shift bound is a good lower bound of the minimum distance for cyclic codes, Reed-Muller codes and geometric Goppa codes. In this paper we consider cyclic codes defined by defining sequence and new simple derivation using the discrete Fourier transform with unknown elements and the Blahut theorem is shown. Moreover two examples of binary cyclic codes are given.

An algorithm for new lower bound of minimum distance by DFT for cyclic codes

For cyclic codes some well-known lower bounds and some decoding methods up to the half of the bounds are suggested. Particularly, the shift bound is a good lower bound of the minimum distance for cyclic codes, Reed-Muller codes and geometric Goppa codes. However, the computational complexity of the shift bound is very large. In this paper we consider cyclic codes defined by their defining set, and a new method of the minimum distance using the discrete Fourier transform(DFT) is shown. Moreover some examples of binary cyclic codes are given.

A decoding method up to the hartmann-tzeng bound using the DFT for cyclic codes

We consider a decoding method for cyclic codes up to the Hartmann-Tzeng bound using the discrete Fourier transform. Indeed we propose how to make a submatrix of the circulant matrix from an error vector for this decoding method. Moreover an example of a binary cyclic code, which could not be corrected by BCH decoding but be correctable by proposed decoding, is given. It is expected that this decoding method induces universal understanding for decoding method up to the Roos bound and the shift bound.

On relationship between proposed lower bound and shift bound for cyclic codes

For cyclic codes we proposed a new lower bound of minimum distance by discrete Fourier transform (DFT). In this paper, we will show relationships between the proposed bound and the shift bound by numerical experiments. Moreover, the computational complexity of proposed lower bound is compared with the shift bound.

A constructing approach of the Roos bound for cyclic codes

A constructing approach for the Roos bound for cyclic codes is given, in order to an alternative derivation and its calculation of the Roos bound using the DFT matrix. Moreover we show three examples in cases of conventional simple approach for the Hartmann-Tzeng bound and the shift bound, and proposed constructing approach.

Computation of the k-Error Linear Complexity of Binary Sequences with Period 2n

The k-error linear complexity(k-LC) of sequences is a very natural and useful generalization of the linear complexity(LC) which has been conveniently used as a measure of unpredictability of pseudorandom sequences, i.e., difficulty in recovering more of a sequence from a short, captured segment. However the effective method for computing the k-LC has been known only for binary sequences with period 2n (Stamp and Martin, 1993). This paper gives an alternative derivation of the Stamp-Martin algorithm. Our method can compute not only k-LC but also an error vector with Hamming weight ≤k which gives the k-LC.

A note a constant weight sequences over q-ary from cyclic difference sets

A method of construction for non- binary periodic sequences from the cyclic difference set is proposed. Two numerical examples are given, and their value distributions and some Hamming distances between self-cyclic shift and cross-cyclic shift of two sequences are evaluated.

On Linear Complexity and Schaub Bound for Cyclic Codes by Defining Sequence with Unknown Elements

The Schaub bound is one of well-known lower bounds of the minimum distance for given cyclic code C, and defined as the minimum value, which is a lower bound on rank of matrix corresponding a codeword, in defining sequence for all sub-cyclic codes of given code C. In this paper, we will try to show relationships between the Schaub bound, the Roos bound and the shift bound from numerical experiments. In order to reduce computational time for the Schaub bound, we claim one conjecture, from numerical examples in binary and ternary cases with short code length that the Schaub bound can be set the value from only defining sequence of given code C.