Some randomized algorithms, used to obtain a random n2 × n2 Sudoku matrix, where n is a natural number, is reviewed in this study. Below is described the set Πn of all (2n) × n matrices, consisting of elements of the set Zn = {1, 2, . . . , n}, such that every row is a permutation. It is proved that such matrices would be particularly useful in developing efficient algorithms in generating Sudo...

The minimum covariance determinant (MCD) method is a robust estimator of multivariate location and scatter (Rousseeuw, 1984). The MCD is highly resistant to outliers, and it is often applied by itself and as a building block for other robust multivariate methods. Computing the exact MCD is very hard, so in practice one resorts to approximate algorithms. Most often the FASTMCD algorithm of Rouss...

In 1964 F.J.Mac Williams introduced the technique of permutation decoding which uses a subset of the automorphism group of the code, a so-called PD-set. A PD-set for a t-error-correcting code C is a set S of automorphisms of the code which is such that, every possible error vector of weight t or less can be moved by some member of S out of the information positions. Concerning the question how ...

MOTIVATION In high-throughput genomic and proteomic experiments, investigators monitor expression across a set of experimental conditions. To gain an understanding of broader biological phenomena, researchers have until recently been limited to post hoc analyses of significant gene lists. METHOD We describe a general framework, significance analysis of function and expression (SAFE), for cond...

In recent years the detailed study of the construction of constant weight codes has been extended from length at most 28 to lengths less than 64. Andries Brouwer maintains web pages with tables of the best known constant weight codes of these lengths. In many cases the codes have more codewords than the best code in the literature, and are not particularly easy to improve. Many of the codes are...

We show that microSIMD architectures are more efficient for media processing than other parallel architectures like SIMD or MIMD parallel processor architectures, and VLIW or superscalar architectures. We define alternative mappings of data onto subwords, and show that the index mapping is an ideal mapping for achieving maximal subword parallelism with minimal revamping of the original serial l...

Permutation codes are error-correcting over symmetric groups. We focus on permutation under Chebyshev (ℓ∞) distance. A code invented by Kløve et al. is of length n, size 2n-d and, minimum distance d. denote the φn,d. This largest known n and d > n/2 so far, to best authors knowledge. They also devised efficient encoding hard-decision decoding (HDD) algorithms that outperform bounded decoding. I...

The hull H(C) of a linear code C is defined by H(C) = C ∩ C⊥. A linear code with a complementary dual (LCD) is a linear code with H(C) = {0}. The dimension of the hull of a code is an invariant under permutation equivalence. For binary and ternary codes the dimension of the hull is also invariant under monomial equivalence and we show that this invariant is determined by the extended weight enu...

Background: We introduce the software that calculates a new statistic that we call the genealogical sorting index, or gsi. This statistic quantifies the common ancestry of groups of individuals on a phylogenetic tree. The significance of an observed genealogical sorting index value is measured with permutation testing. Results: The algorithm for calculating the genealogical sorting index was wr...

In this paper, we study a new combinatorial method to construct decodable binary linear codes for which the automorphism groups are generated by sets of involutory symmetric generators. In this method codewords as elements of a group are represented as permutations in Sn followed by words in the n involutory symmetric generators. Transformation between elements written in symmetric representati...