منابع مشابه
Perfect codes in Doob graphs
We study 1-perfect codes in Doob graphsD(m,n). We show that such codes that are linear over GR(4) exist if and only if n = (4γ+δ−1)/3 andm = (4γ+2δ−4γ+δ)/6 for some integers γ ≥ 0 and δ > 0. We also prove necessary conditions on (m,n) for 1-perfect codes that are linear over Z4 (we call such codes additive) to exist in D(m,n) graphs; for some of these parameters, we show the existence of codes....
متن کاملMDS codes in Doob graphs
Аннотация The Doob graph D(m, n), where m > 0, is the direct product of m copies of The Shrikhande graph and n copies of the complete graph K 4 on 4 vertices. The Doob graph D(m, n) is a distance-regular graph with the same parameters as the Hamming graph H(2m + n, 4). In this paper we consider MDS codes in Doob graphs with code distance d ≥ 3. We prove that if 2m + n > 6 and 2 < d < 2m + n, th...
متن کاملPerfect codes in circulant graphs
A perfect code in a graph Γ = (V,E) is a subset C of V that is an independent set such that every vertex in V \ C is adjacent to exactly one vertex in C. A total perfect code in Γ is a subset C of V such that every vertex of V is adjacent to exactly one vertex in C. A perfect code in the Hamming graph H(n, q) agrees with a q-ary perfect 1-code of length n in the classical setting. A necessary a...
متن کاملℤ2ℤ4-additive perfect codes in Steganography
Steganography is an information hiding application which aims to hide secret data imperceptibly into a cover object. In this paper, we describe a novel coding method based on Z2Z4-additive codes in which data is embedded by distorting each cover symbol by one unit at most (±1-steganography). This method is optimal and solves the problem encountered by the most efficient methods known today, con...
متن کاملOn the intersection of additive perfect codes
The intersection problem for additive (extended and non-extended) perfect codes, i.e. which are the possibilities for the number of codewords in the intersection of two additive codes C1 and C2 of the same length, is investigated. Lower and upper bounds for the intersection number are computed and, for any value between these bounds, codes which have this given intersection value are constructe...
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ژورنال
عنوان ژورنال: Designs, Codes and Cryptography
سال: 2018
ISSN: 0925-1022,1573-7586
DOI: 10.1007/s10623-018-0586-y