By focusing on the families of assignment and permutation problems (such as graph colouring andn-Queens), we show how to adapt D.R. Smith’s KIDS approach for the synthesis of constraint programs (with implicit constraint satisfaction code thus), rather than applicative Refine programs with explicit constraint propagation and pruning code. Synthesis is guided by a global search schema and can be...

For $$m\ge 4$$ even, the duals of p-ary codes, for any prime p, from adjacency matrices m-ary 2-cube $$Q^m_2$$ are shown to have subcodes with parameters $$[m^2,2m-2,m]$$ which minimal PD-sets size $$\frac{m}{2}$$ constructed, hence attaining full error-correction capabilities code, and, as such, most efficient sets permutation decoding.

. In this paper, we consider coding of short data frames (192 bits) by IRA codes. A new interleaver for the IRA codes based on a Gruenbaum graph is proposed. The difference of the proposed algorithm from known methods consists in the following: permutation is performed by using a match smaller interleaver which is derived from the Gruenbaum graph by finding in this graph a Hamiltonian path, enu...

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 ...

The genetic code is well-known to be fault tolerant, in the sense that transcription errors in the third codon position frequently do not influence the amino acid expressed, while errors in other codon positions often lead to amino acids having similar chemical properties. Several articles in the recent past ([?, ?, ?] etc.) have studied the question of optimality of the genetic code. In [?] Di...

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...

We study the computational difficulty of deciding whether two matrices generate equivalent linear codes, i.e., codes that consist of the same codewords up to a fixed permutation on the codeword coordinates. We call this problem Code Equivalence. Using techniques from the area of interactive proofs, we show on the one hand, that under the assumption that the polynomial-time hierarchy does not co...

This paper deals with the amount of disorder that is left in a permutation after one of its elements has been selected with quickselect with or without median-of-three pivoting. Five measures of disorder are considered: inversions, cycles of length less than or equal to some m, cycles of any length, expected cycle length, and the distance to the identity permutation. “Grand averages” for each m...

Authenticated encryption schemes establish both privacy and authenticity. This paper specifies a family of the dedicated authenticated encryption schemes, Artemia. It is an online nonce-based authenticated encryption scheme which supports the associated data. Artemia uses the permutation based mode, JHAE, that is provably secure in the ideal permutation model. The scheme does not require the in...

Let C be a binary extremal self-dual doubly-even code of length n ≥ 48. If such a code has an automorphism σ of prime order p ≥ 5 then the number of fixed points in the permutation action on the coordinates is bounded by the number of p-cycles. It turns out that large primes p, i.e. n − p small, occur extremely rarely in Aut(C). Examples are the extended quadratic residue codes. We prove that d...