lower bound: | 106 |
upper bound: | 108 |
Construction of a linear code [126,5,106] over GF(9): [1]: [127, 5, 107] Linear Code over GF(3^2) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, w, 2, w^3, 0, 0, w^7, 0, w^2, w, w^3, w^7, 1, 1, 2, w, w^6, w^6, 0, 2, 2, w, w^6, w^6, w, w^6, w^3, 1, w^3, w, w^5, 1, w, 2, w^2, 2, 0, 0, w^3, w, w^7, w, w^7, w, w^7, w^5, w, w, w^5, w^2, w^3, 1, w^5, 0, w^3, w^3, w^6, w^6, w^3, 0, w^3, w^5, 1, 0, w^6, 1, w^5, w, w^6, w, w^2, 2, 0, 0, w^3, 1, 0, w^5, w^2, w, w^7, 0, w^2, w^3, 1, w^3, 0, w^5, w^7, 2, w^5, w^6, w^7, w^7, w^2, w^3, 0, w^2, 2, w^7, w^6, w^5, w^2, 1, 0, 2, w^2, 1, 2, 0, w^6, w^7, 1, w^6, w^6, 1, 2, w^5, w^5, w^5, w^5, w^5, w^2, w^2 ] [ 0, 1, 0, 0, 1, w, w^2, w^3, 0, 2, w, 2, w^7, 1, w^6, w^5, w, w, 2, w^2, 1, w^5, w^3, w, w^2, 2, w^5, w^5, w^7, w^2, w^5, w, w^2, 0, w, 1, w^3, w^7, 0, w^5, w^7, w, 2, w^3, 1, 0, 1, w^3, 2, w^5, 0, w, w^7, w^2, w^7, w^3, 2, w^3, 2, w^5, 1, w, 1, w^6, w, w^2, w, w^5, w^2, w^5, w^3, 1, 0, w^6, w^3, w^6, w^7, w^5, w^3, w^2, w, 2, w, w^2, w^6, 0, w^6, w^2, 2, 1, 2, 2, 1, w^3, 1, w^7, w^2, w^2, w^6, w^3, 0, w^2, 2, 0, 1, w^3, w, w^3, w^7, w^2, w^6, w^2, w^3, w, w, w^5, w^3, 0, w^3, w^7, 0, w^7, w^5, w^3, w^6, w^7, w^6 ] [ 0, 0, 1, 0, 2, w^6, w^2, 2, 0, w^6, w^2, 0, w^6, w^6, w^6, w^6, 0, 0, 0, w^2, w, 0, 2, 1, w, 0, w^7, w^6, 1, 2, w^5, w^3, w^7, 1, 0, 1, w, w, w^5, w^6, w^5, 0, w^5, w^5, 1, w^2, w, w, w^3, w^3, w^7, w^2, w^2, 1, w^3, 2, w^3, w^3, w^5, w^6, w, w, 1, w^2, w, w^7, w^5, w^2, 1, w^2, 1, w^3, 2, w^7, w^2, 2, 2, w^5, w^3, w^7, 1, 2, w^5, 1, w^2, 1, w, 0, 2, w^5, w^7, w, w^2, w^6, w^5, w^3, w^2, 1, w^7, w^7, 2, w^6, 1, w^5, 2, w^3, w, w^5, 2, 0, w^2, w, 0, 1, w^5, w^7, 0, w^6, w^6, w^6, w^3, w^2, w^7, 1, w^5, 0, 1 ] [ 0, 0, 0, 1, 1, 2, w^7, w^2, 0, w^6, 2, w^6, w^5, w^2, w^5, 2, 1, 2, w^5, w, w^5, w^2, w^2, 2, 2, w^6, 2, w^6, 1, 1, 2, w^2, w^6, w^3, w^7, w^5, 1, w, w^7, w^5, 2, w^5, w^2, 2, w^2, 2, w^7, w^6, 1, w, w^6, w, w^2, w^6, w^2, w^6, w^6, w, w, w^5, w^6, w, 1, 0, 0, 0, w^5, w^6, w^7, w^5, 2, w^5, w, w^2, w^5, 1, w^3, w^6, w^5, w^7, w^5, 2, 0, 1, w, w^6, w^6, w^5, 0, w, w^5, 2, 2, 2, w^3, w^6, 0, w^5, 1, 2, 1, 1, 1, w, w, 1, w^5, w^7, w, w, 1, w, w^5, 0, w^7, w, w^3, 0, w^7, 1, 2, 0, w^3, 1, w^2, w^6, w ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1 ] where w:=Root(x^2 + 2*x + 2)[1,1]; [2]: [126, 5, 106] Linear Code over GF(3^2) Puncturing of [1] at { 127 } last modified: 2008-09-26
Lb(126,5) = 105 MST Ub(126,5) = 108 follows by a one-step Griesmer bound from: Ub(17,4) = 12 MPa
MST: T. Maruta, M. Shinohara & M. Takenaka, Constructing linear codes from some orbits of projectivities, to appear in Discr. Math.
Notes
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