Related papers: On the number of 1-perfect binary codes: a lower b…

Based on cyclic simplex codes, a new construction of a family of 2-generator quasi-cyclic two-weight codes is given. New optimal binary quasi-cyclic [195, 8, 96], [210, 8, 104] and [240, 8, 120] codes, good QC ternary [195, 6, 126], [208,…

We present a bound on the size of linear codes. This bound is independent of other known bounds, e.g. the Griesmer bound.

We improve Levenshtein's upper bound for the cardinality of a code of length four that is capable of correcting single deletions over an alphabet of even size. We also illustrate that the new upper bound is sharp. Furthermore we construct…

Let $A(n,d)$ (respectively $A(n,d,w)$) be the maximum possible number of codewords in a binary code (respectively binary constant-weight $w$ code) of length $n$ and minimum Hamming distance at least $d$. By adding new linear constraints to…

New bounds on the cardinality of permutation codes equipped with the Ulam distance are presented. First, an integer-programming upper bound is derived, which improves on the Singleton-type upper bound in the literature for some lengths.…

We present novel bounds on the capacity of the independent and identically distributed binary deletion channel. Four upper bounds are obtained by providing the transmitter and the receiver with genie-aided information on suitably-defined…

We consider network coding for networks experiencing worst-case bit-flip errors, and argue that this is a reasonable model for highly dynamic wireless network transmissions. We demonstrate that in this setup prior network error-correcting…

We give a complete classification of binary linear complementary dual codes of lengths up to $13$ and ternary linear complementary dual codes of lengths up to $10$.

A new [48,16,16] optimal linear binary block code is given. To get this code a general construction is used which is also described in this paper. The construction of this new code settles an conjecture mentioned in a 2008 paper by Janosov…

We study properties of binary codes with parameters close to the parameters of 1-perfect codes. An arbitrary binary $(n=2^m-3, 2^{n-m-1}, 4)$ code $C$, i.e., a code with parameters of a triply-shortened extended Hamming code, is a cell of…

Here, we give upper and lower bounds on the count of positive integers $n\le x$ dividing the $n$th term of a nondegenerate linearly recurrent sequence with simple roots.

Best and Brouwer [Discrete Math. 17 (1977), 235-245] proved that triply-shortened and doubly-shortened binary Hamming codes (which have length $2^m-4$ and $2^m-3$, respectively) are optimal. Properties of such codes are here studied,…

In this paper, we study two issues in asynchronous communication systems. The first issue is the derivation of sum capacity bounds for finite dimensional asynchronous systems. In addition, asymptotic results for the sum capacity bounds are…

Multi-class classification is mandatory for real world problems and one of promising techniques for multi-class classification is Error Correcting Output Code. We propose a method for constructing the Error Correcting Output Code to obtain…

An efficient algorithm for classification of binary self-dual codes is presented. As an application, a complete classification of the self-dual codes of length 38 is given.

We give improved lower bounds for binary $3$-query locally correctable codes (3-LCCs) $C \colon \{0,1\}^k \rightarrow \{0,1\}^n$. Specifically, we prove: (1) If $C$ is a linear design 3-LCC, then $n \geq 2^{(1 - o(1))\sqrt{k} }$. A design…

We consider the weight spectrum of a class of quasi-perfect binary linear codes with code distance 4. For example, extended Hamming code and Panchenko code are the known members of this class. Also, it is known that in many cases Panchenko…

We show that any binary $(n=2^m-3, 2^{n-m}, 3)$ code $C_1$ is a part of an equitable partition (perfect coloring) $\{C_1,C_2,C_3,C_4\}$ of the $n$-cube with the parameters $((0,1,n-1,0)(1,0,n-1,0)(1,1,n-4,2)(0,0,n-1,1))$. Now the…

The minimum distance graph of a code has the codewords as vertices and edges exactly when the Hamming distance between two codewords equals the minimum distance of the code. A constructive proof for reconstructibility of an extended perfect…

An alternative proof is given of the existence of greatest lower bounds in the imbalance order of binary maximal instantaneous codes of a given size. These codes are viewed as maximal antichains of a given size in the infinite binary tree…