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on the effect of linear & non-linear texts on students comprehension and recalling
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15 صفحه اولOn 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 کاملExtendability 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 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 کاملOn the extendability of particular classes of constant dimension codes
In classical coding theory, different types of extendability results of codes are known. A classical example is the result stating that every (4, q − 1, 3)-code over an alphabet of order q is extendable to a (4, q, 3)-code. A constant dimension subspace code is a set of (k− 1)-spaces in the projective space PG(n− 1, q), which pairwise intersect in subspaces of dimension upper bounded by a speci...
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ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2001
ISSN: 1071-5797
DOI: 10.1006/ffta.2001.0296