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

被引：2
|
作者：
Dhanalakshmi, R. [1 ]
Durairajan, C. [1 ]
机构：
[1] Bharathidasan Univ, Dept Math, Tiruchirappalli 620024, Tamil Nadu, India
来源：
DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS | 2019年 / 11卷 / 02期
关键词：
Binary Hamming spaces; q-ary Lee spaces; code construction; identifying codes; direct Sum; incomplete hypercubes; BOUNDS;
D O I：
10.1142/S1793830919500277
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study about monotonicity of r-identifying codes in binary Hamming space, q-ary Lee space and incomplete hypercube. Also, we give the lower bounds for M-1,q((<= l)) (n) where M-1,q((<= l)) (n) is the smallest cardinality among all r-identifying codes in Z(q)(n) with respect to the Lee metric. We prove the existence of 1-identifying code in an incomplete hypercube. Also, we give the construction techniques for r-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 M-IH,M-r(k) where M-IH,M-r(k) is the smallest cardinality among all r-identifying codes in an incomplete hypercube with k processors. Also, we give the exact values of M-IH,M-r(k) for small values of r and k (see Sec. 4.3).
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页数：14
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