EFFECTIVE METHOD OF MODIFYING CODE WITH ON-BITS SUMMATION
Annotation
A new principle of modification of codes with summation of on-bits that allows to expand the class of modified codes and obtain codes with better characteristics of low multiplicity error detection is proposed. An overview of known methods of classical codes modifications with summation of individual information bits is presented. A method of constructing modified codes with summation, based on determination of the smallest nonnegative deduction weight incomplete information vector and control of "unused" information bits by using the correction coefficient, which is a convolution modulo two is described; in particular, the correction factor may include discharge, subject to a deduction of the weight. All the possible ways of constructing error-correcting codes modified with the summation are considered. Characteristics of error detection in the information vectors of these codes are analyzed. The conditions, under which a code with summation detects the maximal number of double errors in the information vectors and the conditions under which the code will have the minimum number of monotone non-detectable errors are established. The presented principle of codes modification is shown to allow for increasing the number of well-known codes used in technical diagnostics of discrete systems.
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