r-Identifying codes in binary Hamming space, q-ary Lee space and incomplete hypercube

Author:

Dhanalakshmi R.1,Durairajan C.1ORCID

Affiliation:

1. Department of Mathematics, Bharathidasan University, Tiruchirappalli, Tamilnadu 620024, India

Abstract

We study about monotonicity of [Formula: see text]-identifying codes in binary Hamming space, q-ary Lee space and incomplete hypercube. Also, we give the lower bounds for [Formula: see text] where [Formula: see text] is the smallest cardinality among all [Formula: see text]-identifying codes in [Formula: see text] with respect to the Lee metric. We prove the existence of [Formula: see text]-identifying code in an incomplete hypercube. Also, we give the construction techniques for [Formula: see text]-identifying codes in the incomplete hypercubes in Secs. 4.1 and 4.2. Using these techniques, we give the tables (see Tables 1–6) of upper bounds for [Formula: see text] where [Formula: see text] is the smallest cardinality among all [Formula: see text]-identifying codes in an incomplete hypercube with [Formula: see text] processors. Also, we give the exact values of [Formula: see text] for small values of [Formula: see text] and [Formula: see text] (see Sec. 4.3).

Publisher

World Scientific Pub Co Pte Lt

Subject

Discrete Mathematics and Combinatorics

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Graph theoretic properties of good sets in hypercube;International Journal of Computer Mathematics: Computer Systems Theory;2024-01-02

2. Codes in the q-ary Lee Hypercube;WSEAS TRANSACTIONS ON MATHEMATICS;2022-04-13

3. Progress on fault-tolerant locating-dominating sets;Discrete Mathematics, Algorithms and Applications;2022-04-11

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