For any integer ρ ≥ 1 and for any prime power q, the explicit construction of a infinite family of completely regular (and completely transitive) q-ary codes with d = 3 and with covering radius ρ is given. The intersection array is also computed. Under the same conditions, the explicit construction of an infinite family of q-ary uniformly packed codes (in the wide sense) with covering radius ρ,...

We consider an application to the discrete log problem using completely regular semigroups which may provide a more secure symmetric cryptosystem than the classic system based on groups. In particular we describe a scheme that would appear to offer protection to a standard trial multiplication attack.

J. Rhodes asked during the Chico conference in 1986 for the calculation of joins of semigroup pseudovarieties. This paper proves that the join J∨V of the pseudovariety J of J -trivial semigroups and of any 2-strongly decidable pseudovariety V of completely regular semigroups is decidable. This problem was proposed by the first author for V = G, the pseudovariety of finite groups.

in this paper we introduce continuous $g$-bessel multipliers in hilbert spaces and investigate some of their properties. we provide some conditions under which a continuous $g$-bessel multiplier is a compact operator. also, we show the continuous dependency of continuous $g$-bessel multipliers on their parameters.

A code C is said to be Z2Z4-additive if its coordinates can be partitioned into two subsets X and Y , in such a way that the punctured code of C obtained by removing the coordinates outside X (or, respectively, Y ) is a binary linear code (respectively, a quaternary linear code). The binary image of a Z2Z4-additive code, through the Gray map, is a Z2Z4-linear code, which is not always linear. G...

We generalize the concept of a strong inclusion on a biframe [Sch93] to that of a proximity on a biframe, which is related to the concept of a strong bi-inclusion on a frame introduced in [PP12b]. We also generalize the concept of a bi-compactification of a biframe [Sch93] to that of a compactification of a biframe, and prove that the poset of compactifications of a biframe L is isomorphic to t...

6. M. M. Dragilev, "On compatibly regular bases in nonnuc!ear Kothe spaces," Mat. Zametki, 30, No. 6, 819-822 (1981). P. B. Djakov, "A short proof of the Crone and Robinson theorem on quasiequivalence of regular bases," Stud. Math., 53, No. 3, 269-271 (1975). V. P. Zakharyuta and V. P. Konkdakov, "on the weak equivalence of bases of Kothe spaces," Izv. SKNts, VSh, ~, 12-15 (1983). M. M. Dragile...

In this article the frame-theoretic account of what is archimedean for order-algebraists, and semisimple for people who study commutative rings, deepens with the introduction of J -frames: compact normal frames that are join-generated by their saturated elements. Yosida frames are examples of these. In the category of J -frames with suitable skeletal morphisms, the strongly projectable frames a...

Since their introduction in 1973, completely regular codes have been of interest to coding theorists and graph theorists alike. These highly regular substructures were defined as a generalization of perfect and uniformly packed error-correcting codes but also include many codes having very small minimum distance which are fundamental to the study of distance-regular graphs. While interest in th...

A graph X is said to be End-completely-regular (resp., End-inverse) if its endomorphism monoid End(X) is completely regular (resp., inverse). In this paper, we will show that if X[Y] is End-completely-regular (resp., End-inverse), then both X and Y are End-completely-regular (resp., End-inverse). We give several approaches to construct new End-completely-regular graphs by means of the lexicogra...