A special class of cubic graphs are the cycle permutation graphs. A cycle permutation graph Pn(α) is defined by taking two vertex-disjoint cycles on n vertices and adding a matching between the vertices of the two cycles.In this paper we determine a good upper bound for tenacity of cycle permutation graphs.

We will be considering sets of n-tuples over an alphabet A, in two important cases: A ¡ ¢ 0£ 1¤ (binary code); n¤ , all entries of each word distinct (set of permutations). We often impose closure conditions on these sets, as follows: A binary code is linear if it is closed under coordinatewise addition mod 2. A set of permutations is a group if it is closed under composition. x£ yïs the number...

The permutation associated with the decimal expression of the binary reflected Gray code with N bits is considered. Its cycle structure is studied. Considered as a set of points, its self-similarity is pointed out. As a fractal, it is shown to be the attractor of a IFS. For large values of N the set is examined from the point of view of time series analysis. PACS numbers: 05.45 Df, 05.45 Tp AMS...

We examine the p-ary codes from incidence matrices of Paley graphs P (q) where q ≡ 1 (mod 4) is a prime power, and show that the codes are [ q(q−1) 4 , q − 1, q−1 2 ]2 or [ q(q−1) 4 , q, q−1 2 ]p for p odd. By finding PD-sets we show that for q > 9 the p-ary codes, for any p, can be used for permutation decoding for full error-correction. The binary code from the line graph of P (q) is shown to...

The purpose of this paper is to demonstrate that a distinguisher of Reed-Solomon codes based on the square code construction leads to the cryptanalysis of several cryptosystems relying on them. These schemes are respectively (i) a homomorphic encryption scheme proposed by Bogdanov and Lee; (ii) a variation of the McEliece cryptosystem proposed by Baldi et al. which firstly uses ReedSolomon code...

| An important problem in the theory and application of block code trellises is to nd a coordinate permutation for a given code that minimizes the trellis state complexity. In this paper we show that the problem of minimizing a given component of the state complexity proole is NP-complete. We describe an algorithm, though not guaranteed to nd an optimal coordinate ordering, uses a heuristic des...

A class of geometrically structured quasi-cyclic low-density paritycheck codes with a cylinder structure graph and girth 12 is considered. The parity-check matrix of such a code consists of blocks of zeros and circulant permutation matrices. A class of convolutional codes is assigned to these codes. The convolutional form generator matrix of these codes is obtained by elementary row and column ...

This paper presents a computer program that calculates two effect size estimates (gamma and trimmed-d) that are robust to violations of the assumptions of population normality and homogeneity of variance. Because of their robustness properties, these indices are frequently more appropriate than the conventional parametric indices such as Cohen’s d or Hedges’ g. Additionally, a program that uses...

It is known that there are exactly b t−1 2 c and b t 2c nonequivalent Z2Z4-linear Hadamard codes of length 2t , with α = 0 and α 6= 0, respectively, for all t ≥ 3. In this paper, it is shown that each Z2Z4-linear Hadamard code with α = 0 is equivalent to a Z2Z4-linear Hadamard code with α 6= 0, so there are only b t 2c nonequivalent Z2Z4-linear Hadamard codes of length 2t . Moreover, the orders...