Code Matrices Research Articles

Optimum(n,2)codes for small values of channel error probability (Corresp.)

The generator matrices of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(n, 2)</tex> codes which are optimum for the BSC with sufficiently small channel error probability <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</tex> are given.

A Graph-Theoretic Approach to a Communications Problem

A Graph-Theoretic Approach to a Communications Problem

A search technique for quasi-perfect codes

Using the properties of parity-check matrices of binary linear codes a tree-search program is given which finds quasi-perfect codes. Fixing the number of check digits and the number of errors to be corrected, the program will find one quasi-perfect code for each block length that such a code exists. The efficiency of the search technique is demonstrated by the fact that the program yielded eighteen new quasi-perfect double error-correcting codes.

On codes derivable from the tensor product of check matrices

A class of codes is described having check matrices which are the tensor product of the check matrices of known nonbinary codes and binary codes. The error-correction, error-detection, and error-location capabilities of these codes are specified in terms of the properties of the component codes. The construction procedure allows for a class of codes with a wide variety of redundancies and error-control capabilities. Examples are given of codes from this class which correct random bursts of errors and bursts of bursts of errors.

Nonrandom binary superimposed codes

A binary superimposed code consists of a set of code words whose digit-by-digit Boolean sums (1 + 1 = 1) enjoy a prescribed level of distinguishability. These codes find their main application in the representation of document attributes within an information retrieval system, but might also be used as a basis for channel assignments to relieve congestion in crowded communications bands. In this paper some basic properties of nonrandom codes of this family are presented, and formulas and bounds relating the principal code parameters are derived. Finally, there are described several such code families based upon (1) q -nary conventional error-correcting codes, (2) combinatorial arrangements, such as block designs and Latin squares, (3) a graphical construction, and (4) the parity-check matrices of standard binary error-correcting codes.

Systematic construction of optimal linear recurrent codes for burst error correction

A method is presented for the construction of binary linear burst error correcting recurrent codes of type B2, viz. those codes which correct any burst of lengthl=rb or less provided it is confined amongr successive blocks of lengthb. The proposed codes are optimal in the sense they meet the lower bound obtained by Wyner and Ash, and are constructed through a particular bordering of the characteristic matrices of analogous codes of shorter block length. Finally, existing linear recurrent codes are compared for efficiency.