On the Existence of Perfect Linear Codes over Z4 with Respect to Homogeneous Weight
نویسندگان
چکیده
In this paper, we investigate the existence problem of perfect linear codes over the ring Z4 of integers modulo 4 with respect to homogenous metric. Mathematics Subject Classification: 94B05; 94B60
منابع مشابه
Linear Codes over Galois Ring GR(p2, r) Related to Gauss sums
Linear codes over finite rings become one of hot topics in coding theory after Hommons et al.([4], 1994) discovered that several remarkable nonlinear binary codes with some linear-like properties are the images of Gray map of linear codes over Z4. In this paper we consider two series of linear codes C(G) and C̃(G) over Galois ring R = GR(p2,r), where G is a subgroup of R(s) ∗ and R(s) = GR(p2,rs...
متن کاملPerfect 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 کاملIsometries and Binary Images of Linear Block Codes over Z4+uZ4 and Z8+uZ8
Let F2 be the binary field and Z2r the residue class ring of integers modulo 2 , where r is a positive integer. For the finite 16-element commutative local Frobenius nonchain ring Z4 + uZ4, where u is nilpotent of index 2, two weight functions are considered, namely the Lee weight and the homogeneous weight. With the appropriate application of these weights, isometric maps from Z4 + uZ4 to the ...
متن کاملOptimal Linear Codes over Z
We examine the main linear coding theory problem and study the structure of optimal linear codes over the ring Zm. We derive bounds on the maximum Hamming weight of these codes. We give bounds on the best linear codes over Z8 and Z9 of lengths up to 6. We determine the minimum distances of optimal linear codes over Z4 for lengths up to 7. Some examples of optimal codes are given.
متن کاملOn the Covering Radius of Codes over Z4 with Chinese Euclidean Weight
In this paper, we give lower and upper bounds on the covering radius of codes over the ring Z4 with respect to chinese euclidean distance. We also determine the covering radius of various Repetition codes, Simplex codes Type α and Type β and give bounds on the covering radius for MacDonald codes of both types over Z4.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012