lower bound:  112 
upper bound:  113 
Construction of a linear code [232,9,112] over GF(2): [1]: [64, 3, 56] Linear Code over GF(2^3) BCHCode over GF(8) with parameters 63 55 [2]: [448, 9, 224] Linear Code over GF(2) ConcatenatedCode of [1] and [6] [3]: [4, 1, 4] Cyclic Linear Code over GF(2) RepetitionCode of length 4 [4]: [4, 3, 2] Cyclic Linear Code over GF(2) Dual of the RepetitionCode of length 4 [5]: [8, 4, 4] Quasicyclic of degree 2 Linear Code over GF(2) PlotkinSum of [4] and [3] [6]: [7, 3, 4] Linear Code over GF(2) Shortening of [5] at 1 [7]: [64, 4, 55] Linear Code over GF(2^3) BCHCode over GF(8) with parameters 63 54 [8]: [448, 12, 220] Linear Code over GF(2) ConcatenatedCode of [7] and [6] [9]: [455, 12, 224] Linear Code over GF(2) ConstructionX using [8] [2] and [6] [10]: [231, 11, 112] Linear Code over GF(2) generalized residue code of [9] puncturing at the support of a word of weight 224 [11]: [232, 11, 112] Linear Code over GF(2) PadCode [10] by 1 [12]: [232, 9, 112] Linear Code over GF(2) Subcode of [11] last modified: 20010130
Lb(232,9) = 112 is found by taking a subcode of: Lb(232,11) = 112 is found by lengthening of: Lb(231,11) = 112 EB1 Ub(232,9) = 113 follows by a onestep Griesmer bound from: Ub(118,8) = 56 otherwise adding a parity check bit would contradict: Ub(119,8) = 57 DMa
EB1: Y. Edel & J. Bierbrauer, Some codes related to BCH codes of low dimension, preprint, 1995.
Notes
