lower bound:  26 
upper bound:  28 
Construction of a linear code [72,16,26] over GF(2): [1]: [6, 6, 1] Cyclic Linear Code over GF(2) UniverseCode of length 6 [2]: [3,0] Code ZeroCode of length 3 [3]: [63, 16, 23] "BCH code (d = 21, b = 42)" Linear Code over GF(2) BCHCode with parameters 63 21 42 [4]: [66, 16, 23] Linear Code over GF(2) DirectSum of [3] and [2] [5]: [2, 2, 1] Cyclic Linear Code over GF(2) CordaroWagnerCode of length 2 [6]: [65, 11, 27] Linear Code over GF(2) Let C1 be the BCHCode over GF( 2) of parameters 63 42. Let C2 the SubcodeBetweenCode of dimension 11 between C1 and the BCHCode with parameters 63 25. Return ConstructionX using C1, C2 and [5] [7]: [66, 11, 28] Linear Code over GF(2) ExtendCode [6] by 1 [8]: [66, 18] Linear Code over GF(2) The Vector space sum: [7] + [4] [9]: [66, 17] Linear Code over GF(2) ExpurgateCode [8] [10]: [72, 17, 25] Linear Code over GF(2) ConstructionX using [9] [7] and [1] [11]: [73, 17, 26] Linear Code over GF(2) ExtendCode [10] by 1 [12]: [72, 16, 26] Linear Code over GF(2) Shortening of [11] at { 73 } last modified: 20010130
Lb(72,16) = 26 is found by shortening of: Lb(73,17) = 26 is found by adding a parity check bit to: Lb(72,17) = 25 XX Ub(72,16) = 28 follows by a onestep Griesmer bound from: Ub(43,15) = 14 is found by considering shortening to: Ub(38,10) = 14 otherwise adding a parity check bit would contradict: Ub(39,10) = 15 Bou
XX:
Notes
