lower bound: | 24 |
upper bound: | 26 |
Construction of a linear code [40,7,24] over GF(4): [1]: [44, 8, 27] Linear Code over GF(2^2) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 1, w^2, w, 1, w, w, w^2, 1, 1, 1, 0, w^2, w, w^2, w^2, w, 0, w, w^2, 0, w^2, w, w, w^2, w, 0, 1, 1, 1, w, w^2, w^2, 1, w^2, w, 1 ] [ 0, 1, 0, 0, 0, 0, 0, 0, w, 0, 0, 0, w, 1, w^2, 1, w^2, w^2, 1, 1, 0, w^2, w, 0, w, w^2, w^2, w^2, 1, 0, 1, w^2, 0, w, w, w^2, w^2, w, w^2, w, 1, 0, 0, w^2 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, w, 0, 0, 0, w, 1, w^2, 1, w^2, w^2, 1, 1, 0, w^2, w, 0, w, w^2, w^2, w^2, 1, 0, 1, w^2, 0, w, w, w^2, w^2, w, w^2, w, 1, 0, w^2 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, w, 0, 0, 0, w, 1, w^2, 1, w^2, w^2, 1, 1, 0, w^2, w, 0, w, w^2, w^2, w^2, 1, 0, 1, w^2, 0, w, w, w^2, w^2, w, w^2, w, 1, w^2 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 1, w^2, w, w^2, w, w, w^2, w^2, 0, w, 1, 0, 1, w, w, w, w^2, 0, w^2, w, 0, 1, 1, w, w, 1, w, 1, w^2, 0, 0, 0, w^2, 0, 0, w ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, w^2, w, w^2, w, w, w^2, w^2, 0, w, 1, 0, 1, w, w, w, w^2, 0, w^2, w, 0, 1, 1, w, w, 1, w, 1, w^2, 0, 0, 0, w^2, 0, w ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, w^2, w, w^2, w, w, w^2, w^2, 0, w, 1, 0, 1, w, w, w, w^2, 0, w^2, w, 0, 1, 1, w, w, 1, w, 1, w^2, 0, 0, 0, w^2, w ] [ 0, 0, 0, 0, 0, 0, 0, 1, w^2, w, 1, w, w, w^2, 1, 1, 1, 0, w^2, w, w^2, w^2, w, 0, w, w^2, 0, w^2, w, w, w^2, w, 0, 1, 1, 1, w, w^2, w^2, 1, w^2, w, 1, 1 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [41, 8, 24] Linear Code over GF(2^2) Puncturing of [1] at { 42 .. 44 } [3]: [40, 7, 24] Linear Code over GF(2^2) Shortening of [2] at { 41 } last modified: 2001-12-17
Lb(40,7) = 24 is found by shortening of: Lb(41,8) = 24 is found by truncation of: Lb(44,8) = 27 Zi Ub(40,7) = 26 follows by a one-step Griesmer bound from: Ub(13,6) = 6 is found by considering shortening to: Ub(10,3) = 6 GH
Zi: Thomas Rehfinger, N. Suresh Babu & Karl-Heinz Zimmermann, New Good Codes via CQuest -- A System for the Silicon Search of Linear Codes, pp 294-306 in: Algebraic Combinatorics and Applications, A. Betten et al., eds, Springer, 2001.
Notes
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