We study -length Abelian codes over Galois rings with characteristic , where and are relatively prime, having the additional structure of being closed under the following two permutations: i) permutation effected by multiplying the coordinates with a unit in the appropriate mixed-radix representation of the coordinate positions and ii) shifting the coordinates by positions. A code is -quasi-cyc...

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...

Let E be an n -dimensional vector space. Then the symmetric group Sym ( ) acts on by permuting elements of a basis and hence r -fold tensor product ? . Bowman, Doty Martin ask, in [1] , whether endomorphism algebra End is cellular. The module permutation for certain Young -set. We shall show that arbitrary -set cellular algebra. determine, terms point stabilisers which appear, when quasi-heredi...

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.

In this paper, we consider Bayesian estimation and model determination for two-way contingency tables. The analysis is based on partitioning the parameter space of a saturated log-linear model into parameter subspaces identiied by considering the natural symmetries of the data. Prior distributions may then be chosen to respect invariance restrictions required by the available prior information....

We introduce the notion of quasi-Feistel network, which is generalization of the Feistel network, and contains the Lai-Massey scheme as an instance. We show that some of the works on the Feistel network, including the works of Luby-Rackoff, Patarin, Naor-Reingold and Piret, can be naturally extended to our setting. This gives a new proof for theorems of Vaudenay on the security of the Lai-Masse...

We introduce a Gray map from F2m + uF2m to F 2m 2 and study (1 + u)-constacyclic codes over F2m + uF2m ,where u 2 = 0. It is proved that the image of a (1+u)-constacyclic code length n overF2m+uF2m under the Gray map is a distance-invariant quasi-cyclic code of indexm and length 2mn over F2. We also prove that every code of length 2mnwhich is the Gray image of cyclic codes overF2m+uF2m of lengt...

The current study focuses on the problem of determining investment attrаctiveness of countries by means of monitoring regional stock markets. The method of using the permutation entropy as a model of investment attractiveness estimation is suggested. We have calculated the permutation entropy for the time series of stock markets of countries for the period from 2005 to 2018. The countries with ...