C&SA | Contents

Volume 62 >>> № 2 MARCH — APRIL 2026

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UDC 621.396

Y. Nikolaychuk
West Ukrainian National University, Ternopil, Ukraine,
ymnykolaychuk@gmail.com

I. Pitukh
West Ukrainian National University, Ternopil, Ukraine,
pirom75@ukr.net

V. Hryha
Vasyl Stefanyk Carpathian National University, Ivano-Frankivsk, Ukraine,
v.dr_2000@ukr.net

Y. Bezgachnyuk
Ivano-Frankivsk National Technical University of Oil and Gas, Ivano-Frankivsk, Ukraine,
b_yurkovskiy@ukr.net

METHOD AND ALGORITHM FOR INTERBASE CONVERSION OF BINARY RADEMAKER
CODES INTO CRESTENSON REDUNDANCY CODES

Abstract. The relevance of developing methods and tools for inter-basis conversions of large-bit numbers represented in binary Rademacher codes, Rademacher–Crestenson and Haar–Crestenson residue codes of the residue class system (RCS) is substantiated. The aim of the research is to develop a method and algorithm for converting large-bit numbers represented by binary codes of the Rademacher basis (R) into the corresponding residue codes of the Rademacher–Crestenson (R–C) and Haar–Crestenson (H–C) bases. The mathematical foundations of existing algorithms and tools for converting large-bit binary R-codes into residue codes (R–C) and (H–C) are analyzed. As a result, it was established that the basic components of the mathematical operations of converting binary R-codes of the Rademacher basis into (R–C) and (H–C) residue codes of the Crestenson basis are parallel operations of convolution of R-codes according to the system of mutually prime modules of the SCL. A new method and algorithm for inter-base conversion of large-bit binary R-codes into (R–C)- and (H–C)-residue codes are proposed. Examples of the implementation of the proposed method and algorithm in the data encoding range within 32-bit binary codes are given. The characteristics of parallelization and execution speed for addition and multiplication operations in (R–C)- and (H–C)-codes are studied. A software model for the study and implementation of inter-base conversion of R-codes into (R–C)- and (H–C)-codes in the Python programming language is developed.

Keywords: Rademacher binary codes, Haar–Crestenson, Rademacher–Crestenson residue codes, algorithm, number-theoretic bases.

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UDC 621.396

METHOD AND ALGORITHM FOR INTERBASE CONVERSION OF BINARY RADEMAKER CODES INTO CRESTENSON REDUNDANCY CODES

REFERENCES

METHOD AND ALGORITHM FOR INTERBASE CONVERSION OF BINARY RADEMAKER
CODES INTO CRESTENSON REDUNDANCY CODES