On optimal ternary linear codes of dimension 6
نویسندگان
چکیده
منابع مشابه
Some New Optimal Ternary Linear Codes
Let d3(n, k) be the maximum possible minimum Hamming distance of a ternary [n, k, d; 3]-code for given values of n and k. It is proved that d3(44, 6) = 27, d3(76, 6) = 48, d3(94, 6) = 60, d3(124, 6) = 81, d3(130, 6) = 84, d3(134, 6) = 87, d3(138, 6) = 90, d3(148, 6) = 96, d3(152, 6) = 99, d3(156, 6) = 102, d3(164, 6) = 108, d3(170, 6) = 111, d3(179, 6) = 117, d3(188, 6) = 123, d3(206, 6) = 135,...
متن کاملOptimal Linear Codes Over GF(7) and GF(11) with Dimension 3
Let $n_q(k,d)$ denote the smallest value of $n$ for which there exists a linear $[n,k,d]$-code over the Galois field $GF(q)$. An $[n,k,d]$-code whose length is equal to $n_q(k,d)$ is called {em optimal}. In this paper we present some matrix generators for the family of optimal $[n,3,d]$ codes over $GF(7)$ and $GF(11)$. Most of our given codes in $GF(7)$ are non-isomorphic with the codes pre...
متن کاملSome new results for optimal ternary linear codes
Let ( ) be the maximum possible minimum Hamming distance of a ternary [ ]-code for given values of and . We describe a package for code extension and use this to prove some new exact values of ( ). Moreover, we classify the ternary [ ( )]-codes for some values of and .
متن کاملOptimal Linear Codes of Dimension 4 over GF(5)
[48] __, " On complexity of trellis structure of linear block codes, " IEEE [49] T. Klgve, " Upperbounds on codes correcting asymmebic errors, " IEEE [SO] __, " Minimum support weights of binary codes, " IEEE Trans. Inform. [53] A. Lafourcade and A. Vardy, " Asymptotically good codes have infinite trellis comwlexitv. " IEEE Duns. issue on " Codes and Finite Geometries "). [59] __, " The shift b...
متن کاملTernary Linear Codes and Quadrics
For an [n, k, d]3 code C with gcd(d, 3) = 1, we define a map wG from Σ = PG(k − 1, 3) to the set of weights of codewords of C through a generator matrix G. A t-flat Π in Σ is called an (i, j)t flat if (i, j) = (|Π ∩ F0|, |Π ∩ F1|), where F0 = {P ∈ Σ | wG(P ) ≡ 0 (mod 3)}, F1 = {P ∈ Σ | wG(P ) 6≡ 0, d (mod 3)}. We give geometric characterizations of (i, j)t flats, which involve quadrics. As an a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Mathematics of Communications
سال: 2011
ISSN: 1930-5346
DOI: 10.3934/amc.2011.5.505