منابع مشابه
Extendability of linear codes over Fq
For an [n, k, d]q code C, we define a mapping wC from PG(k − 1, q) to the set of weights of C via a generator matrix of C. We give a geometric aspect derived from wC to investigate the extendability of linear codes. We survey known extension theorems and some recent results.
متن کاملOn the (2,1)-extendability of ternary linear codes
We show that every [n, k, d]3 code with diversity (Φ0, Φ1), 3 ≤ k ≤ 5, gcd(d, 3) = 1, is (2, 1)-extendable except for the case (Φ0, Φ1) = (40, 36) for k = 5, and that an [n, 5, d]3 code with diversity (40, 36), gcd(d, 3) = 1, is (2, 1)-extendable if Ad ≤ 50. Geometric conditions for the (2, 1)-extendability of not necessarily extendable [n, k, d]3 codes for k = 5, 6 are also given.
متن کاملSome improvements to the extendability of ternary linear codes
For a ternary [n, k, d] code C with d ≡ 1 or 2 (mod 3), k 3, the diversity (Φ0,Φ1) given by Φ0 = 1 2 ∑ 3|i, i =0 Ai, Φ1 = 1 2 ∑ i ≡0, d (mod 3) Ai is important to know about the extendability of C, where Ai stands for the number of codewords with weight i. As a continuation of [T. Maruta, Extendability of ternary linear codes, Des. Codes Cryptogr. 35 (2005) 175–190], we prove all the conjecture...
متن کاملThe nonexistence of some quaternary linear codes of dimension 5
We prove the nonexistence of linear codes with parameters [400; 5; 299]4, [401; 5; 300]4, [405; 5; 303]4, [406; 5; 304]4, [485; 5; 363]4 and [486; 5; 364]4 attaining the Griesmer bound. For that purpose we give a characterization of linear codes with parameters [86; 4; 64]4, [101; 4; 75]4, [102; 4; 76]4 and [122; 4; 91]4. c © 2001 Elsevier Science B.V. All rights reserved.
متن کاملOne - Generator Quasi - Cyclic Quaternary Linear Codes and Construction X
Let GF (q) denote the Galois field of q elements, and let V (n, q) denote the vector space of all ordered n-tuples over GF (q). The number of nonzero positions in a vector x ∈ V (n, q) is called the Hamming weight wt(x) of x. The Hamming distance d(x,y) between two vectors x,y ∈ V (n, q) is defined by d(x,y) = wt(x − y). A linear code C of length n and dimension k over GF (q) is a k-dimensional...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2005
ISSN: 0012-365X
DOI: 10.1016/j.disc.2004.08.031