lower bound: | 104 |
upper bound: | 105 |
Construction of a linear code [216,9,104] over GF(2): [1]: [4, 1, 4] Cyclic Linear Code over GF(2) RepetitionCode of length 4 [2]: [4, 3, 2] Cyclic Linear Code over GF(2) Dual of the RepetitionCode of length 4 [3]: [8, 4, 4] Quasicyclic of degree 2 Linear Code over GF(2) PlotkinSum of [2] and [1] [4]: [7, 3, 4] Linear Code over GF(2) Shortening of [3] at 1 [5]: [64, 4, 55] Linear Code over GF(2^3) BCHCode over GF(8) with parameters 63 54 [6]: [63, 4, 54] Linear Code over GF(2^3) Puncturing of [5] at 1 [7]: [441, 12, 116] Linear Code over GF(2) ConcatenatedCode of [6] and [4] [8]: [217, 11, 104] Linear Code over GF(2) generalized residue code of [7] puncturing at the support of a word of weight 224 [9]: [216, 10, 104] Linear Code over GF(2) Shortening of [8] at { 217 } [10]: [216, 9, 104] Linear Code over GF(2) Subcode of [9] last modified: 2001-01-30
Lb(216,9) = 104 is found by taking a subcode of: Lb(216,10) = 104 is found by shortening of: Lb(217,11) = 104 EB1 Ub(216,9) = 105 follows by a one-step Griesmer bound from: Ub(110,8) = 52 follows by a one-step Griesmer bound from: Ub(57,7) = 26 otherwise adding a parity check bit would contradict: Ub(58,7) = 27 vT3
vT3: H.C.A. van Tilborg, The smallest length of binary 7-dimensional linear codes with prescribed minimum distance, Discr. Math. 33 (1981) 197-207.
Notes
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