lower bound: | 21 |
upper bound: | 21 |
Construction of a linear code [36,6,21] over GF(3): [1]: [1, 1, 1] Cyclic Linear Code over GF(3^2) UniverseCode of length 1 over GF(9) [2]: [8, 2, 7] "BCH code (d = 7, b = 1)" Linear Code over GF(3^2) BCHCode over GF(9) with parameters 8 7 [3]: [8, 3, 6] "BCH code (d = 6, b = 1)" Linear Code over GF(3^2) BCHCode over GF(9) with parameters 8 6 [4]: [9, 3, 7] Linear Code over GF(3^2) ConstructionX using [3] [2] and [1] [5]: [121, 116, 3] "Hamming code (r = 5)" Linear Code over GF(3) 5-th order HammingCode over GF( 3) [6]: [121, 5, 81] Cyclic Linear Code over GF(3) Dual of [5] [7]: [119, 5, 79] Linear Code over GF(3) Puncturing of [6] at { 120 .. 121 } [8]: [40, 4, 27] Linear Code over GF(3) ResidueCode of [7] [9]: [38, 4, 25] Linear Code over GF(3) Puncturing of [8] at { 39 .. 40 } [10]: [13, 3, 9] Linear Code over GF(3) ResidueCode of [9] [11]: [11, 3, 7] Linear Code over GF(3) Puncturing of [10] at { 12 .. 13 } [12]: [4, 2, 3] Linear Code over GF(3) ResidueCode of [11] [13]: [36, 6, 21] Linear Code over GF(3) ZinovievCode using inner codes: [12], outer codes: [4] last modified: 2003-10-07
Lb(36,6) = 21 BZ Ub(36,6) = 21 follows by a one-step Griesmer bound from: Ub(14,5) = 7 follows by a one-step Griesmer bound from: Ub(6,4) = 2 is found by considering shortening to: Ub(5,3) = 2 is found by construction B: [consider deleting the (at most) 3 coordinates of a word in the dual]
Notes
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