lower bound: | 53 |
upper bound: | 53 |
Construction of a linear code [84,7,53] over GF(3): [1]: [1, 1, 1] Cyclic Linear Code over GF(3) RepetitionCode of length 1 [2]: [121, 116, 3] "Hamming code (r = 5)" Linear Code over GF(3) 5-th order HammingCode over GF( 3) [3]: [121, 5, 81] Cyclic Linear Code over GF(3) Dual of [2] [4]: [119, 5, 79] Linear Code over GF(3) Puncturing of [3] at { 120 .. 121 } [5]: [40, 4, 27] Linear Code over GF(3) ResidueCode of [4] [6]: [38, 4, 25] Linear Code over GF(3) Puncturing of [5] at { 39 .. 40 } [7]: [13, 3, 9] Linear Code over GF(3) ResidueCode of [6] [8]: [11, 3, 7] Linear Code over GF(3) Puncturing of [7] at { 12 .. 13 } [9]: [4, 2, 3] Linear Code over GF(3) ResidueCode of [8] [10]: [80, 6, 51] "BCH code (d = 51, b = 80)" Linear Code over GF(3) BCHCode with parameters 80 51 80 [11]: [80, 5, 53] "BCH code (d = 53, b = 1)" Linear Code over GF(3) BCHCode with parameters 80 53 1 [12]: [80, 7, 50] "BCH code (d = 50, b = 1)" Linear Code over GF(3) BCHCode with parameters 80 50 1 [13]: [85, 7, 54] Linear Code over GF(3) ConstructionXX using [12] [11] [10] [9] and [1] [14]: [84, 7, 53] Linear Code over GF(3) Puncturing of [13] at { 85 } last modified: 2001-12-17
Lb(84,7) = 53 is found by truncation of: Lb(85,7) = 54 XX Ub(84,7) = 53 follows by a one-step Griesmer bound from: Ub(30,6) = 17 is found by considering truncation to: Ub(28,6) = 15 HHM
XX:
Notes
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