lower bound: | 114 |
upper bound: | 118 |
Construction of a linear code [248,13,114] over GF(2): [1]: [4, 1, 4] Cyclic Linear Code over GF(2) RepetitionCode of length 4 [2]: [4, 3, 2] Cyclic Linear Code over GF(2) Dual of the RepetitionCode of length 4 [3]: [8, 4, 4] Quasicyclic of degree 2 Linear Code over GF(2) PlotkinSum of [2] and [1] [4]: [8, 7, 2] Cyclic Linear Code over GF(2) Dual of the RepetitionCode of length 8 [5]: [16, 11, 4] Linear Code over GF(2) PlotkinSum of [4] and [3] [6]: [15, 11, 3] Linear Code over GF(2) Puncturing of [5] at 1 [7]: [9, 5, 3] Linear Code over GF(2) Shortening of [6] at { 1, 2, 3, 4, 5, 6 } [8]: [16, 2, 15] Linear Code over GF(2^4) Shortening of [11] at { 17 } [9]: [240, 8, 120] Linear Code over GF(2) ZinovievCode using inner codes: [14], outer codes: [8] [10]: [16, 1, 16] Cyclic Linear Code over GF(2) RepetitionCode of length 16 [11]: [17, 3, 15] "BCH code (d = 15, b = 2)" Linear Code over GF(2^4) BCHCode over GF(16) with parameters 17 15 2 [12]: [16, 3, 14] Linear Code over GF(2^4) Puncturing of [11] at { 17 } [13]: [15, 5, 7] "BCH code (d = 7, b = 1)" Linear Code over GF(2) BCHCode with parameters 15 7 [14]: [15, 4, 8] "BCH code (d = 8, b = 15)" Linear Code over GF(2) BCHCode with parameters 15 8 0 [15]: [240, 13, 112] Linear Code over GF(2) ZinovievCode using inner codes: [14] [13], outer codes: [12] [10] [16]: [249, 13, 115] Linear Code over GF(2) ConstructionX using [15] [9] and [7] [17]: [250, 13, 116] Linear Code over GF(2) ExtendCode [16] by 1 [18]: [248, 13, 114] Linear Code over GF(2) Puncturing of [17] at { 249 .. 250 } last modified: 2001-01-30
Lb(248,13) = 114 is found by truncation of: Lb(250,13) = 116 is found by adding a parity check bit to: Lb(249,13) = 115 XB Ub(248,13) = 118 follows by a one-step Griesmer bound from: Ub(129,12) = 59 Ja
XB:
Notes
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