lower bound: | 103 |
upper bound: | 103 |
Construction of a linear code [120,4,103] over GF(8): [1]: [121, 4, 104] Linear Code over GF(2^3) code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, w^5, w^5, 0, 0, w^3, w^3, w^6, w^6, 1, 1, w^5, w^4, 0, w^4, w^5, w^6, w, w^5, w^4, w^2, w^4, w^2, w^3, w^3, w, w^5, w^3, 1, w^5, 1, 1, 1, w^5, w^3, 1, 1, w^4, 0, w^3, 1, w^4, w^6, w, w^4, w^4, w^4, w, w^2, 1, w, 1, w^6, w^5, w^5, w^2, w^2, w^5, w, w, 0, w, w^2, w^3, w^4, w, w^3, w, w^3, w^5, w^4, w, w^6, w^6, w^2, w^6, w^5, 1, 1, w^3, w^3, w^4, 0, w, w, 0, w^3, w^3, 0, w^2, w^3, w^4, w^4, w^6, w^4, w^2, 0, w^3, 0, w^3, w, w, 1, w, 0, 1, 1, w^5, w^4, w, w^5, 1, w^4, 0, w^5, w^5 ] [ 0, 1, 0, 0, 0, 0, 0, 0, w, w, w^2, w^2, 1, 1, w^4, w^4, 0, w, w^6, w^5, w^3, 1, w, w^2, w, w^3, w^3, w^3, w^2, 1, w^2, w^2, w^2, w^6, w^4, 1, w^5, 1, w^4, w, w^6, w^5, 0, 1, w^3, w^3, w^6, w^4, w^4, w^6, w^4, w^6, w^4, w^5, w^2, w, 1, w^4, w^3, w, w^4, w, w, w^3, 1, 1, w^6, w^2, 0, w^5, w^3, 1, w^4, w^4, w^2, w^6, w^6, w^6, w^2, w^4, w^2, 1, w^3, w^6, w^5, w^6, w^3, 1, 0, w^3, w^3, 0, w^6, w, 1, w^3, 0, w^4, w^6, w^2, 1, w^2, 0, w, w, 0, w, w^4, 0, w^2, w, w^3, w^6, w, w^3, w^6, w^4, w^5, w^5, 0, w^2 ] [ 0, 0, 1, 1, 0, 0, w^4, w^4, w^4, w^4, w^2, w^2, w^3, w^3, w^4, w^4, w^3, 1, w^5, w^5, w, w^6, 0, w^5, w^3, 0, w^5, 1, 1, w^4, w^6, 0, w^3, w^3, w, w^2, w^3, w^5, 0, w^2, w^2, 1, w^6, w, w^4, w^2, w^6, w^6, w^5, 0, w^2, w^5, w^2, 1, 1, w^3, w, 0, 1, 0, w^5, w^2, 1, w^2, w^6, w^2, 0, w^6, w^6, w^3, w^4, w^5, w, w^6, w^3, w^2, w^3, w^6, 0, w^6, w^5, w^5, w^5, 0, w^5, w^6, w, w^4, w^6, 0, w^4, w^3, w^2, 0, w^3, 1, 1, w^4, w^5, w^2, w^6, 1, w^4, w^3, w^4, 0, 1, 1, w^5, w, w, w^3, 1, w^5, w^6, w^4, w^3, w^6, w^2, w^2, w^4 ] [ 0, 0, 0, 0, 1, 1, w^5, w^5, w^6, w^6, 1, 1, w^3, w^3, 1, 1, w, w, w^3, 1, 0, w^6, w^3, w, 0, w, w^6, w^3, w^2, w^4, 0, w^6, w^4, w^5, w^6, w^2, w^6, w^5, w^5, w^5, 0, w^5, w^2, w, w^2, w^4, 1, w, 0, w^2, w^3, w^3, w^3, w^5, w^2, 0, w, w^5, w^3, w^3, 0, w^5, w, w^4, w^6, w^2, w^2, 0, w^2, w^6, w^2, w^5, w^6, w, w^4, 0, w^5, 1, w^6, w, w, w^5, w^6, w^2, 1, 1, 0, w^4, w^2, w, w^2, w, 0, w^3, w^3, w^3, 0, 1, w^3, 1, w^6, w^2, w^5, 0, w^6, 1, w, w^4, w^4, w^5, 1, 1, w^6, w^2, w^5, w, w^2, w^3, w, w^6, w^3 ] where w:=Root(x^3 + x + 1)[1,1]; [2]: [120, 4, 103] Linear Code over GF(2^3) Puncturing of [1] at { 121 } last modified: 2006-06-27
Lb(120,4) = 103 is found by truncation of: Lb(121,4) = 104 Koh Ub(120,4) = 103 follows by a one-step Griesmer bound from: Ub(16,3) = 12 Hi4
Koh: Axel Kohnert, email, 2006.
Notes
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