An algorithm is presented that solves the initial vector problem for group codes for the Gaussian channel. The Gaussian channel is a communications model in which messages are represented by vectors in R and transmitted over a noisy channel. In this paper, the set of messages, called a code, is generated by a group of permutation matrices and the problem of finding the code with the largest min...

Equidistant Frequency Permutation Arrays are combinatorial objects of interest in coding theory. A frequency permutation array is a type of constant composition code in which each symbol occurs the same number of times in each codeword. The problem is to find a set of codewords such that any pair of codewords are a given uniform Hamming distance apart. The equidistant case is of special interes...

In this paper, we explore the theory and expand upon practice of fitness landscape analysis for optimization problems over space permutations. Many computational analytical tools analysis, such as distance correlation, require identifying a metric measuring similarity different solutions to problem. We begin with survey available metrics permutations, then use principal component classify these...

We develop a new perspective on the unique maximal decomposition of an arbitrary affine permutation into a product of cyclically decreasing elements, implicit in work of Thomas Lam [Lam06]. This decomposition is closely related to the affine code, which generalizes the kbounded partition associated to Grassmannian elements. We also prove that the affine code readily encodes a number of basic co...

Recently Genetic algorithms are successfully used for decoding some classes of error correcting codes. For decoding a linear block code C, these genetic algorithms computes a permutation π of the code generator matrix depending of the received word. Our main contribution in this paper is to choose the permutation π from the automorphism group of C. This choice allows reducing the complexity of ...

In this paper we study the security of the key of compact McEliece schemes based on alternant/Goppa codes with a non-trivial permutation group, in particular quasicyclic alternant codes. We show that it is possible to reduce the key-recovery problem on the original quasi-cyclic code to the same problem on a smaller code derived from the public key. This result is obtained thanks to the invarian...

A computer code and algorithm are developed for the computer perception of molecular symmetry. The code generates and uses the Euclidian distance matrices of molecular structures to generate the permutationinversion group of the molecule. The permutation-inversion group is constructed as the automorphism group of the Euclidian distance matrix. Applications to several molecular structures and fu...

A full diversity block space-time code over two transmit antennas and two symbol periods is introduced. The proposed method results in substantial performance improvement over the widely used scheme of Alamouti [1] and at the same time allows for a simple maximum likelihood decoding algorithm.

Visontai conjectured in 2013 that the joint distribution of ascent and distinct nonzero value numbers on the set of subexcedant sequences is the same as that of descent and inverse descent numbers on the set of permutations. This conjecture has been proved by Aas in 2014, and the generating function of the corresponding bistatistics is the double Eulerian polynomial. Among the techniques used b...

We show how to use the elements of a sharply k-transitive permutation group of degree n to form error-correcting codes, as suggested by Blake [1], presenting suitable decoding algorithms for these codes. In particular, we concentrate on using the Mathieu group M12 to form a (12,95040,8)-code to correct three errors. The algorithm we give for this code differs from that given by Cohen and Deza [2].