lower bound:  29 
upper bound:  31 
Construction of a linear code [40,6,29] over GF(8): [1]: [40, 6, 29] Linear Code over GF(2^3) extension of a quasicyclic code found by Plamen Hristov Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 1, w^3, 0, 1, w, w^2, w^5, w^5, w^2, w, 1, 0, w^3, 1, w^4, w^4, 1, 0, 0, w^4, w^3, w^3, w^3, w^4, w^2, w^5, 1, w, w^6, w^5, w^5, w^4, 1, w^4 ] [ 0, 1, 0, 0, 0, 0, w^3, w^2, w^3, w^3, w^5, w^6, w^4, w^6, 0, w, 1, 1, w^6, w^6, 0, w^5, w^6, 1, 0, 1, w^3, w^4, w^4, w, 1, w^4, w^2, w^5, w^4, w^5, w^6, w^4, w^4, w^3 ] [ 0, 0, 1, 0, 0, 0, w^6, w^5, w^2, w^4, w, w^6, w^3, 0, w^5, 1, w^5, 1, w^6, w^3, w^4, w^3, w, w^6, 1, w^3, w^6, w^5, w, w^6, 0, w^5, w^3, w^6, 0, 0, 1, w^4, w^3, w^5 ] [ 0, 0, 0, 1, 0, 0, w^6, 1, w^5, 1, w^5, 0, w^3, w^6, w, w^4, w^2, w^5, w^6, w^3, 0, w^6, w^4, w, w^6, w, w^5, 1, w^3, 1, w^5, w^4, w, w, w, w^4, w^4, w, 1, w^5 ] [ 0, 0, 0, 0, 1, 0, w^6, 1, 1, w, 0, w^6, w^4, w^6, w^5, w^3, w^3, w^2, w^3, w^5, 0, w^3, 0, w^4, w, w^4, w^4, w^3, w^6, 0, w^3, 1, w^3, w^3, w^6, w^2, 0, w^6, 0, w^6 ] [ 0, 0, 0, 0, 0, 1, w^3, 0, 1, w, w^2, w^5, w^5, w^2, w, 1, 0, w^3, 1, w^4, w^4, 1, 0, 0, w^4, w^3, w^3, w^3, w^4, w^2, w^5, 1, w, w^6, w^5, w^5, w^4, 1, 0, 1 ] where w:=Root(x^3 + x + 1)[1,1]; last modified: 20080123
Lb(40,6) = 28 is found by taking a subcode of: Lb(40,7) = 28 GW2 Ub(40,6) = 31 is found by considering shortening to: Ub(37,3) = 31 is found by considering truncation to: Ub(34,3) = 28 Mas
Mas:
Notes
