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Method and Algorithm for Interbase Conversion of Rademacher Binary Codes into Christensen Residue Codes
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DOI：10.1007/s10559-026-00860-9.png)
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Abstract
En 中文
The relevance of developing methods and means for interbase conversion of multi-digit numbers represented in Rademacher binary codes, Rademacher-Christensen and Haar-Christensen residue codes of the residue class system (RCS) is substantiated. The aim of the research is to develop a method and algorithm for converting multi-digit numbers represented by Rademacher (R) basis binary codes into corresponding residue codes of the Rademacher-Christensen (R-C) and Haar-Christensen (H-C) bases. The mathematical foundations of the available algorithms and means of converting multi-digit binary R-codes into (R-C) and (H-C) residue codes are analyzed. As a result, it is proved that the basic components of mathematical operations for converting Rademacher basis binary R-codes into Christensen basis (R-C) and (H-C) residue codes are parallel operations of R-code convolution using a system of mutually prime RCS modules. A new method and algorithm for interbase conversion of multi-digit binary R-codes into (R-C) and (H-C) residue codes are proposed. Examples of implementing the proposed method and algorithm in the data encoding range within 32-bit binary codes are provided. The characteristics of parallelization and performance of addition and multiplication operations in (R-C) and (H-C) codes are analyzed. A software model for investigating and implementing interbase conversion of R-codes into (R-C) and (H-C) codes in the Python programming language has been constructed.
Keywords:
Rademacher binary codes
Haar-Christensen residue codes
Rademacher-Christensen
algorithm
theoretical number bases
Journal
C
IF:
0.6
Papers:
56
Citations:
0
