Search results for "permuta"

Binary Hamming codes and Boolean designs

2021

AbstractIn this paper we consider a finite-dimensional vector space $${\mathcal {P}}$$ P over the Galois field $${\text {GF}}(2),$$ GF ( 2 ) , and the family $${\mathcal {B}}_k$$ B k (respectively, $${\mathcal {B}}_k^*$$ B k ∗ ) of all the k-sets of elements of $$\mathcal {P}$$ P (respectively, of $${\mathcal {P}}^*= {\mathcal {P}} \setminus \{0\}$$ P ∗ = P \ { 0 } ) summing up to zero. We compute the parameters of the 3-design $$({\mathcal {P}},{\mathcal {B}}_k)$$ ( P , B k ) for any (necessarily even) k, and of the 2-design $$({\mathcal {P}}^{*},{\mathcal {B}}_k^{*})$$ ( P ∗ , B k ∗ ) for any k. Also, we find a new proof for the weight distribution of the binary Hamming code. Moreover, we…

Comparison of discretization strategies for the model-free information-theoretic assessment of short-term physiological interactions

2023

This work presents a comparison between different approaches for the model-free estimation of information-theoretic measures of the dynamic coupling between short realizations of random processes. The measures considered are the mutual information rate (MIR) between two random processes [Formula: see text] and [Formula: see text] and the terms of its decomposition evidencing either the individual entropy rates of [Formula: see text] and [Formula: see text] and their joint entropy rate, or the transfer entropies from [Formula: see text] to [Formula: see text] and from [Formula: see text] to [Formula: see text] and the instantaneous information shared by [Formula: see text] and [Formula: see…

A Hardware and Secure Pseudorandom Generator for Constrained Devices

2018

Hardware security for an Internet of Things or cyber physical system drives the need for ubiquitous cryptography to different sensing infrastructures in these fields. In particular, generating strong cryptographic keys on such resource-constrained device depends on a lightweight and cryptographically secure random number generator. In this research work, we have introduced a new hardware chaos-based pseudorandom number generator, which is mainly based on the deletion of an Hamilton cycle within the $N$ -cube (or on the vectorial negation), plus one single permutation. We have rigorously proven the chaotic behavior and cryptographically secure property of the whole proposal: the mid-term eff…

Multiply Transitive Permutation Groups

1982

Since the beginnings of finite group theory, the multiply transitive permutation groups have exercised a certain fascination. This is mainly due to the fact that apart from the symmetric and alternating groups not many of them were known. Only very recently final results about multiply transitive permutation groups have been proved, using the classification of all finite simple groups (see 7.5).

On finite products of totally permutable groups

1996

In this paper the structure of finite groups which are the product of two totally permutable subgroups is studied. In fact we can obtain the -residual, where is a formation, -projectors and -normalisers, where is a saturated formation, of the group from the corresponding subgroups of the factor subgroups.

A class of imprimitive groups

2010

We classify imprimitive groups inducing the alternating group A4 on the set of blocks, with the inertia subgroup satisfying some very natural geometrical conditions which force the group to operate linearly.

Homomorphs and wreath product extensions

1982

A homomorph is a class of (finite soluble) groups closed under the operation Q of taking epimorphic images. (All groups considered in this paper are finite and soluble.) Among those types of homomorphs that have found particular interest in the theory of finite soluble groups are formations and Schunck classes; the reader is referred to (2), § 2, for a definition of those classes. In the present paper we are interested in homomorphs satisfying the following additional closure property:(W0) if A is abelian with elementary Sylow subgroups, then each wreath product A G (with respect to an arbitrary permutation representation of G) with G ∊ is contained in .

Some contributions to the theory of transformation monoids

2019

The aim of this paper is to present some contributions to the theory of finite transformation monoids. The dominating influence that permutation groups have on transformation monoids is used to describe and characterise transitive transformation monoids and primitive transitive transformation monoids. We develop a theory that not only includes the analogs of several important theorems of the classical theory of permutation groups but also contains substantial information about the algebraic structure of the transformation monoids. Open questions naturally arising from the substantial paper of Steinberg [A theory of transformation monoids: combinatorics and representation theory. Electron. J…

Permutation properties and the fibonacci semigroup

1989

Fitting classes and products of totally permutable groups

2002

The second and third authors have been supported by Proyecto PB 97-0674-C02-02 of DGESIC, Ministerio de Educación y Cultura, Spain.