A Testing Set for Preparata-Like Codes

IF 0.58 Q3 Engineering

Journal of Applied and Industrial Mathematics Pub Date : 2023-08-07 DOI:10.1134/S1990478923020205

A. Yu. Vasil’eva

引用次数: 0

Abstract

The reconstruction of an object of a given class by its intersection with some (so-called testing) set is studied. For the class, we consider Preparata-like codes, i.e., nonlinear codes of length \( n=2^{2m}-1 \), \( m=2,3,\dots \), with code distance 5 and twice the size of a linear code of the same length and distance. Conditions are determined under which the union of a few concentric spheres forms a testing set for Preparata-like codes.

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类准备代码的测试集

研究了给定类对象与某个(所谓的测试)集的交集对其进行重构的问题。对于该类，我们考虑类prepare码，即长度为\( n=2^{2m}-1 \), \( m=2,3,\dots \)的非线性码，码距为5，是相同长度和距离的线性码的两倍。确定了几个同心球的并集构成拟备码测试集的条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Applied and Industrial Mathematics Engineering-Industrial and Manufacturing Engineering

CiteScore

1.00

自引率

0.00%

发文量

期刊介绍： Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.