ON THE APPLICABILITY OF ALGEBRAIC CODE PROPERTIES TO IMPROVE THE EFFICIENCY OF COMPUTER SYSTEM PROTECTION
A. A. Pavlov, Yu. A. Romanenko, O. F. Pashayev, F.A. Pavlov, A. N. Tsar’kov, A. Yu. Romanenko · Vestnik komp iuternykh i informatsionnykh tekhnologii · 2025
The Hamming code is most widely used to correct single errors that occur in computing systems. As a result of the studies, shortcomings of its use were identified, associated with the lack of the ability to control the logical operation of inversion and correction of errors of greater multiplicity. The need to develop a correcting code with increased correcting capacity that controls the logical operation of inversion is substantiated. A statement is formulated that allows controlling the inversion operation using the Hamming code, taking into account the following rule for forming check bits: the i-check bit is inverted if the i-row of the information part of the check matrix contains an odd number of ones, if it has an even number of ones, then the value of the i-check bit does not change. A statement has been formulated that allows detecting double errors by the Hamming code, when performing a logical inversion operation, the parity check value is formed according to the rule: for an even number of information bits, the parity check has the same value as the parity check of the direct values of the information bits, and for an odd number, it has an inverse value. An algorithm has been developed for constructing a correction code that controls the logical inversion operation without changing the values of the check bits, with the following properties: – has a code distance of d = 3; – the number of check bits of the code rk is equal to the number of check bits rх of the Hamming code; – allows correcting errors in direct and inverse values of the code set. An algorithm has been developed for constructing an algebraic linear code with increased correcting capacity, for which rules have been formulated for grouping error syndrome bits into bits that determine: – a block of information bits containing an error; – an erroneous bit in a 3-bit information block. A decoding algorithm has been developed that generates the values of the error syndrome bits, defining the address of the information block containing the error and the number of the erroneous bit in the three-bit information block; The developed code ensures correction of: – single errors in information bits; – multiple errors in check bits; – errors in direct and inverse values of the code set without changing the values of the check bits.