In this paper, we derive analytic expressions for the success probability of decoding (Partial) Unit Memory codes in memoryless channels. An applications of this result is that these codes outperform individual block codes in certain channels.

Using double counting, we prove Delsarte inequalities for qary codes and their improvements. Applying the same technique to q-ary constant-weight codes, we obtain new inequalities for q-ary constantweight codes.

For λ an n-th power of a unit in a finite chain ring we prove that λ-constacyclic repeated-root codes over some finite chain rings are equivalent to cyclic codes. This allows us to simplify the structure of some constacylic codes. We also study the α+pβconstacyclic codes of length p over the Galois ring GR(p, r).

In article present measure code distance algorithm of binary and ternary linear block code using block Korkin-Zolotarev (BKZ). Proved the upper bound on scaling constant for measure code distance of non-systematic linear block code using BKZ-method for different value of the block size. Introduced method show linear decrease of runtime from number of threads and work especially good under not d...

In this paper we give two families of codes which are minimal generators of biinfmite langüages: the family of very thin codes (which contains the rational codes) and another family containing the circular codes. We propose the conjecture that ail codes are minimal generators. Résumé. Dans cet article, nous exhibons deux familles de codes qui sont générateurs minimaux du langage de mots bi-infi...

We study some combinatorial and algorithmic properties of discriminating codes in bipartite graphs. In particular, we provide bounds on minimum discriminating codes and give constructions. We also show that upperbounding the size of a discriminating code is NP-complete.

It has been shown that a complex orthogonal design that provides full diversity and full transmission rate for a space–time block code is not possible for more than two antennas. Previous attempts have been concentrated in generalizing orthogonal designs which provide space–time block codes with full diversity and a high transmission rate. In this work, we design rate one codes which are quasi-...

In this paper we studied generalization of Hermitian function field proposed by A.Garcia and H.Stichtenoth. We calculated a Weierstrass semigroup of the point at infinity for the case q=2, r>=3. It turned out that unlike Hermitian case, we have already three generators for the semigroup. We then applied this result to codes, constructed on generalized Hermitian function fields. Further, we appl...

Let R = Z4[u]/〈u〉 = Z4 + uZ4 + . . . + uZ4 (u = 0) where k ∈ Z satisfies k ≥ 2. For any odd positive integer n, it is known that cyclic codes over R of length n are identified with ideals of the ring R[x]/〈x − 1〉. In this paper, an explicit representation for each cyclic code over R of length n is provided and a formula to count the number of codewords in each code is given. Then a formula to c...