lower bound: | 116 |
upper bound: | 118 |
Construction of a linear code [244,11,116] over GF(2): [1]: [18, 9, 6] Linear Code over GF(2) Extend the QRCode over GF(2)of length 17 [2]: [7,0] Code ZeroCode of length 7 [3]: [64, 1, 64] Cyclic Linear Code over GF(2^3) BCHCode over GF(8) with parameters 63 59 [4]: [448, 3, 256] Linear Code over GF(2) ConcatenatedCode of [3] and [11] [5]: [455, 3, 256] Linear Code over GF(2) DirectSum of [4] and [2] [6]: [64, 3, 56] Linear Code over GF(2^3) BCHCode over GF(8) with parameters 63 55 [7]: [448, 9, 224] Linear Code over GF(2) ConcatenatedCode of [6] and [11] [8]: [4, 1, 4] Cyclic Linear Code over GF(2) RepetitionCode of length 4 [9]: [4, 3, 2] Cyclic Linear Code over GF(2) Dual of the RepetitionCode of length 4 [10]: [8, 4, 4] Quasicyclic of degree 2 Linear Code over GF(2) PlotkinSum of [9] and [8] [11]: [7, 3, 4] Linear Code over GF(2) Shortening of [10] at 1 [12]: [64, 4, 55] Linear Code over GF(2^3) BCHCode over GF(8) with parameters 63 54 [13]: [448, 12, 220] Linear Code over GF(2) ConcatenatedCode of [12] and [11] [14]: [455, 12, 224] Linear Code over GF(2) ConstructionX using [13] [7] and [11] [15]: [473, 12, 230] Linear Code over GF(2) ConstructionX using [14] [5] and [1] [16]: [243, 11, 115] Linear Code over GF(2) ResidueCode of [15] [17]: [244, 11, 116] Linear Code over GF(2) ExtendCode [16] by 1 last modified: 2001-03-30
Lb(244,11) = 116 EB1 Ub(244,11) = 118 follows by a one-step Griesmer bound from: Ub(125,10) = 58 otherwise adding a parity check bit would contradict: Ub(126,10) = 59 Ja
Ja: D.B. Jaffe, Binary linear codes: new results on nonexistence, 1996, code.ps.gz.
Notes
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