Minimum distances of error-correcting codes in incidence rings.
-T-quasigroup codes with one check symbol and their error detection capabilities
It is well known that there exist some types of the most frequent errors made by human operators during transmission of data which it is possible to detect using a code with one check symbol. We prove that there does not exist an -T-code that can detect all single, adjacent transposition, jump transposition, twin, jump twin and phonetic errors over an alphabet that contains 0 and 1. Systems that detect all single, adjacent transposition, jump transposition, twin, jump twin errors and almost all...
Nonassociative algebras: some applications.
Nonassociative algebras can be applied, either directly or using their particular methods, to many other branches of Mathematics and other Sciences. Here emphasis will be given to two concrete applications of nonassociative algebras. In the first one, an application to group theory in the line of the Restricted Burnside Problem will be considered. The second one opens a door to some applications of non-associative algebras to Error correcting Codes and Cryptography.
Note on Gray Codes for Permutation Lists
On codes with finite interpreting delay : a defect theorem
On codes with finite interpreting delay: a defect theorem
We introduce two new classes of codes, namely adjacent codes and codes with finite interpreting delay. For each class, we establish an extension of the defect theorem.
On codes with given minimum distance and covering radius.
On codes with given minimum distance and covering radius.
On distance nonregularity of Preparata codes.
On extremal additive codes of length to
In this paper we consider the extremal even self-dual -additive codes. We give a complete classification for length . Under the hypothesis that at least two minimal words have the same support, we classify the codes of length and we show that in length such a code is equivalent to the unique -hermitian code with parameters [18,9,8]. We construct with the help of them some extremal -modular lattices.
On full partial quasigroups of finite order and local cardinal maximum codes.
On Group and Nongroup Perfect Codes in q Symbols.
On mixed codes with covering radius 1 and minimum distance 2.
On Multiple Deletion Codes
In 1965 Levenshtein introduced the deletion correcting codes and found an asymptotically optimal family of 1-deletion correcting codes. During the years there has been a little or no research on t-deletion correcting codes for larger values of t. In this paper, we consider the problem of finding the maximal cardinality L2(n;t) of a binary t-deletion correcting code of length n. We construct an infinite family of binary t-deletion correcting codes. By computer search, we construct t-deletion codes...
On perfect-like binary and non-binary linear codes - a brief survey.
On some subsemigroups of a free semigroup.
On the minimum distance of ideals in group algebras
On the Non-Existence of Certain M.D.S. Codes and Projective Planes.
On the number of zero trace elements in polynomial bases for F2n.
Let Fq denote the finite field of q elements. O. Ahmadi and A. Menezes have recently considered the question about the possible number of elements with zero trace in polynomial bases of F2n over F2. Here we show that the Weil bound implies that there is such a basis with n + O(log n) zero-trace elements.
Penny-Packing and Two-Dimensional Codes.