lower bound: | 36 |
upper bound: | 38 |
Construction of a linear code [48,6,36] over GF(8): [1]: [48, 6, 36] Linear Code over GF(2^3) Code found by Plamen Hristov Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, w^4, w^2, w^3, w, w^3, w^2, w^3, w^4, 1, w^5, w^3, w^3, 1, w, w^6, w^6, w^2, w, w^5, 1, 0, w^6, w^3, w^5, w^5, w, 1, w^6, w, w, 1, w^3, w^3, w^2, w^6, w^6, w^5, w^4, w^2, w^6, 0, 0 ] [ 0, 1, 0, 0, 0, 0, w^3, w^2, 0, w, w^4, 1, 0, 0, w^3, w^5, w^3, w^5, w^4, 0, w^6, w, w^5, w^6, w^2, w, 1, w^5, 1, w^6, 1, w^4, w^5, w^4, w^2, w^3, w^5, w^6, w^5, 1, w^3, w, 0, w^4, w, w^5, w^5, w^4 ] [ 0, 0, 1, 0, 0, 0, w^3, 1, 0, 1, w^4, w^2, w^6, w^3, w^6, w^6, w^3, w^5, w, w^5, w^5, w^6, 0, w^4, w^3, 1, w, w^4, w^3, w^5, w^3, 0, w^3, 0, w^5, w^6, w^4, w^3, 1, w^6, w^4, w^2, w^6, w^2, w^5, 1, 0, w^4 ] [ 0, 0, 0, 1, 0, 0, w^2, w, w^3, w^6, w^3, w^5, w^4, 1, w^2, w^4, w^5, 1, 0, w^5, 1, w, w^2, w^6, w^6, w^2, 1, w^2, w^2, 0, w^2, w^4, w^5, w^6, w^6, w, w, w^2, 1, 0, w^3, 0, w^2, 0, w^2, w^4, w^6, w^2 ] [ 0, 0, 0, 0, 1, 0, w^4, 0, 1, 1, w^4, w^5, w^2, 0, 0, w^3, w^6, w^2, 0, w, w, w^6, w^4, w^4, w, w^2, w^2, w^2, w^5, w^3, w^5, w^4, w^5, w, w^5, w^5, w^3, 1, w^5, w^6, w^6, w^4, w^3, w^3, w, w, w^2, 0 ] [ 0, 0, 0, 0, 0, 1, w^5, w^6, w^4, w^6, w^5, w^6, 1, w^3, w, w^6, w^6, w^3, w^4, w^2, w^3, w^5, w^4, w, w^3, 0, w^2, w^6, w, w, w^4, w^3, w^2, w^4, w^4, w^3, w^6, w^6, w^5, w^2, w^2, w^2, 0, 0, w^3, w^3, w^3, w^3 ] where w:=Root(x^3 + x + 1)[1,1]; last modified: 2008-02-01
Lb(48,6) = 35 is found by shortening of: Lb(49,7) = 35 is found by truncation of: Lb(58,7) = 44 DaH Ub(48,6) = 38 is found by considering shortening to: Ub(45,3) = 38 is found by considering truncation to: Ub(43,3) = 36 Hi4
Hi4: R. Hill, Optimal linear codes, pp. 75-104 in: Cryptography and Coding II (C. Mitchell, ed.), Oxford Univ. Press, 1992.
Notes
|