Tsonka Stefanova Baicheva

Optimal binary one-error-correcting codes of length 10 have 72 codewords

The maximum number of codewords in a binary code with length n and minimum distance d is denoted by A(n, d). By construction it is known that A(10, 3)/spl ges/72 and A(11, 3)/spl ges/144. These bounds have long been conjectured to be the exact values. This is here proved by classifying various codes of smaller length and lengthening these using backtracking and isomorphism rejection. There are 562 inequivalent codes attaining A(10, 3)=72 and 7398 inequivalent codes attaining A(11, 3)=144.

On the cyclic redundancy-check codes with 8-bit redundancy

Polynomials of degree eight over GF(2) which are suitable to be used as generator polynomials for cyclic redundancy-check (CRC) codes are investigated. Their minimum distance, properness and undetected error probability for binary symmetric channels (BSCs) are compared with the existing ATM standard. Covering radii and the weight distributions of the leaders of cosets are given for all examined codes.

Determination of the Best CRC Codes with up to 10-Bit Redundancy

All binary polynomials of degree up to 10 which are suitable to be used as generator polynomials of CRC codes are classified and all the necessary data for the evaluation of the error control performance of the CRC codes generated by the classified polynomials is calculated. A procedure, based on the computed data, for choosing the best CRC code is suggested.

On the performance of the ternary [13, 7, 5] quadratic-residue code

We investigate the weight structure and error-correcting performance of the ternary [13, 7, 5] quadratic-residue code. It is shown that the covering radius of the code is equal to three and it is t-proper for error correction for any t=0, 1, 2. Two decoding algorithms are suggested.

Covering radii of ternary linear codes of small dimensions and codimensions

The covering radii and the least covering radii of all two- and three-dimensional codes over GF(3) are given in the present work. The exact values of the least covering radii of some ternary linear codes of codimensions up to 8 are also determined, and a table of values of t/sub 3/[n,k] for n/spl les/27 is presented.

Binary and Ternary Linear Quasi-Perfect Codes With Small Dimensions

The aim of this work is a systematic investigation of the possible parameters of quasi-perfect (QP) binary and ternary linear codes of small dimensions and preparing a complete classification of all such codes. First, we give a list of infinite families of QP codes which includes all binary, ternary, and quaternary codes known to us. We continue further with a list of sporadic examples of binary and ternary QP codes. Later we present the results of our investigation where binary QP codes of dimensions up to 14 and ternary QP codes of dimensions up to 13 are classified.

On the covering radius of ternary negacyclic codes with length up to 26

The covering radius of all ternary negacyclic codes of even length up to 26 is given. The minimum distances and weight distributions of all codes were recalculated. Seven of the open cases for the least covering radius of ternary linear codes were solved and for the other three cases upper bounds were improved.

Classification of optimal (v, 4, 1) binary cyclically permutable constant-weight codes and cyclic 2-(v, 4, 1) designs with v ≤ 76

We classify up to isomorphism optimal (v, 4, 1) binary cyclically permutable constantweight (CPCW) codes with v ≤ 76 and cyclic 2-(73, 4, 1) and 2-(76, 4, 1) designs. There is a one-to-one correspondence between optimal (v, 4, 1) CPCW codes, optimal cyclic binary constant-weight codes with weight 4 and minimum distance 6, (v, 4; ⌎(v − 1)/12⌏) difference packings, and optimal (v, 4, 1) optical orthogonal codes. Therefore, the classification of CPCW codes holds for them too. Perfect (v, 4, 1) CPCWcodes are equivalent to (v, 4, 1) cyclic difference families, and thus (73, 4, 1) cyclic difference families are classified too.

The Covering Radius of Ternary Cyclic Codes with Lengthup to 25

The covering radius of all ternary cyclic codes of length up to 25 is given. Some of the results were obtained by computer and for others mathematical reasonings were applied. The minimal distances of all codes were recalculated.

Optimal \((v,5,2,1)\) optical orthogonal codes of small \(v\)

Abstract We classify up to multiplier equivalence optimal