lower bound: | 32 |
upper bound: | 32 |
Construction of a linear code [78,13,32] over GF(2): [1]: [10, 3, 8] Linear Code over GF(2^3) Extended BCHCode over GF(8) with parameters 9 7 2 [2]: [10, 5, 4] Linear Code over GF(2) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 1, 1, 1, 0 ] [ 0, 1, 0, 0, 0, 1, 0, 1, 1, 0 ] [ 0, 0, 1, 0, 0, 1, 1, 0, 1, 0 ] [ 0, 0, 0, 1, 0, 1, 1, 1, 0, 0 ] [ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ] [3]: [8, 4, 4] Quasicyclic of degree 2 Linear Code over GF(2) Construction from a stored generator matrix: [ 1, 0, 0, 0, 1, 1, 1, 0 ] [ 0, 1, 0, 0, 0, 1, 1, 1 ] [ 0, 0, 1, 0, 1, 0, 1, 1 ] [ 0, 0, 0, 1, 1, 1, 0, 1 ] [4]: [8, 1, 8] Cyclic Linear Code over GF(2) RepetitionCode of length 8 [5]: [80, 14, 32] Linear Code over GF(2) ZinovievCode using inner codes: [4] [3], outer codes: [2] [1] [6]: [78, 13, 32] Linear Code over GF(2) Shortening of [5] at { 33, 73 } last modified: 2001-01-31
Lb(78,13) = 32 To Ub(78,13) = 32 follows by a one-step Griesmer bound from: Ub(45,12) = 16 follows by a one-step Griesmer bound from: Ub(28,11) = 8 otherwise adding a parity check bit would contradict: Ub(29,11) = 9 Ja
To: L.M.G.M. Tolhuizen, On the optimal use and the construction of linear block codes, Master's Thesis, Dept. of Math. and Comp. Sc., Eindhoven Univ. of Techn., The Netherlands, Nov. 1986.
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