lower bound: | 112 |
upper bound: | 116 |
Construction of a linear code [244,13,112] over GF(2): [1]: [5, 5, 1] Cyclic Linear Code over GF(2) UniverseCode of length 5 [2]: [16, 2, 15] Linear Code over GF(2^4) Shortening of [5] at { 17 } [3]: [240, 8, 120] Linear Code over GF(2) ZinovievCode using inner codes: [8], outer codes: [2] [4]: [16, 1, 16] Cyclic Linear Code over GF(2) RepetitionCode of length 16 [5]: [17, 3, 15] "BCH code (d = 15, b = 2)" Linear Code over GF(2^4) BCHCode over GF(16) with parameters 17 15 2 [6]: [16, 3, 14] Linear Code over GF(2^4) Puncturing of [5] at { 17 } [7]: [15, 5, 7] "BCH code (d = 7, b = 1)" Linear Code over GF(2) BCHCode with parameters 15 7 [8]: [15, 4, 8] "BCH code (d = 8, b = 15)" Linear Code over GF(2) BCHCode with parameters 15 8 0 [9]: [240, 13, 112] Linear Code over GF(2) ZinovievCode using inner codes: [8] [7], outer codes: [6] [4] [10]: [245, 13, 113] Linear Code over GF(2) ConstructionX using [9] [3] and [1] [11]: [246, 13, 114] Linear Code over GF(2) ExtendCode [10] by 1 [12]: [244, 13, 112] Linear Code over GF(2) Puncturing of [11] at { 245 .. 246 } last modified: 2001-01-30
Lb(244,13) = 112 is found by truncation of: Lb(246,13) = 114 is found by adding a parity check bit to: Lb(245,13) = 113 XB Ub(244,13) = 116 follows by a one-step Griesmer bound from: Ub(127,12) = 58 follows by a one-step Griesmer bound from: Ub(68,11) = 29 follows by a one-step Griesmer bound from: Ub(38,10) = 14 otherwise adding a parity check bit would contradict: Ub(39,10) = 15 Bou
XB:
Notes
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