lower bound: | 139 |
upper bound: | 140 |
Construction of a linear code [213,6,139] over GF(3): [1]: [9,0] Code ZeroCode of length 9 [2]: [9, 1, 9] Cyclic Linear Code over GF(3) RepetitionCode of length 9 [3]: [12, 6, 6] Linear Code over GF(3) Extend the QRCode over GF(3)of length 11 [4]: [9, 3, 6] Linear Code over GF(3) Shortening of [3] at { 10 .. 12 } [5]: [27, 4, 18] Linear Code over GF(3) PlotkinSum of [4] [2] and [1] [6]: [192, 2, 144] Quasicyclic of degree 24 Linear Code over GF(3) QuasiCyclicCode of length 192 with generating polynomials: x^7 + 2*x^6 + 2*x^4 + 2*x^3 + x^2 + 1, 2*x^6 + 2*x^5 + x^4 + x^2 + x + 2, x^7 + 2*x^6 + 2*x^4 + 2*x^3 + x^2 + 1, x^7 + 2*x^6 + 2*x^4 + 2*x^3 + x^2 + 1, x^6 + x^5 + 2*x^4 + 2*x^2 + 2*x + 1, 2*x^7 + 2*x^5 + 2*x^4 + x^3 + x + 1, x^6 + x^5 + 2*x^4 + 2*x^2 + 2*x + 1, x^7 + x^6 + 2*x^5 + 2*x^3 + 2*x^2 + x, 2*x^7 + 2*x^6 + x^5 + x^3 + x^2 + 2*x, x^6 + x^5 + 2*x^4 + 2*x^2 + 2*x + 1, x^7 + x^5 + x^4 + 2*x^3 + 2*x + 2, x^6 + x^5 + 2*x^4 + 2*x^2 + 2*x + 1, x^6 + x^5 + 2*x^4 + 2*x^2 + 2*x + 1, x^7 + 2*x^6 + 2*x^4 + 2*x^3 + x^2 + 1, 2*x^7 + 2*x^6 + x^5 + x^3 + x^2 + 2*x, 2*x^7 + x^6 + x^4 + x^3 + 2*x^2 + 2, x^7 + x^6 + 2*x^5 + 2*x^3 + 2*x^2 + x, 2*x^6 + 2*x^5 + x^4 + x^2 + x + 2, 2*x^7 + 2*x^5 + 2*x^4 + x^3 + x + 1, 2*x^7 + x^6 + x^4 + x^3 + 2*x^2 + 2, x^7 + 2*x^6 + 2*x^4 + 2*x^3 + x^2 + 1, x^7 + x^5 + x^4 + 2*x^3 + 2*x + 2, x^7 + x^6 + 2*x^5 + 2*x^3 + 2*x^2 + x, x^7 + x^5 + x^4 + 2*x^3 + 2*x + 2 [7]: [192, 6, 126] Quasicyclic of degree 24 Linear Code over GF(3) QuasiCyclicCode of length 192 with generating polynomials: x^7 + 2*x^6 + 1, 2*x^7 + x^6 + 2*x^5 + 2*x^3 + 2*x^2 + 2, x^7 + x^6 + 2*x^5 + 2*x^2 + 2*x + 1, x^7 + 2*x^6 + 2*x^5 + x^4 + 2*x + 2, x^7 + 2*x^5 + x^3 + 2*x^2 + x + 1, 2*x^7 + x^5 + x^4 + 2*x + 2, x^7 + x^6 + x^5 + x^3 + 1, 2*x^6 + x^5 + 2*x^3 + x^2 + 2*x, 2*x^6 + x^3 + 2*x, x^7 + x^6 + 2*x^5 + x^3 + x + 1, 2*x^7 + x^6 + x^5 + 2*x^4 + x^3 + x^2 + 1, x^7 + 2*x^5 + 2*x^4 + x^3 + 2*x^2 + x, x^7 + x^5 + 2*x^4 + x^3 + 2*x^2, x^7 + x^6 + 2*x^2 + 1, 2*x^6 + 2*x^5 + x^4 + x^3 + x + 1, 2*x^7 + 2*x^2 + 2, 2*x^6 + 2*x^4 + 2*x^3 + x^2 + x + 2, 2*x^7 + 2*x^3 + x^2 + x + 2, x^7 + 2*x^6 + x^5 + x^4 + 2*x^3 + 2*x^2 + 2*x + 2, 2*x^7 + 2*x^4 + 2*x^2 + 1, x^7 + 2*x^6 + x^4 + 2, 2*x^7 + x^6 + x^5 + x^4 + x^3 + x^2, x^6 + x^5 + 2*x^3 + 2*x, 2*x^7 + x^6 + 2*x^4 + x^3 + x^2 + 2*x + 1 [8]: [219, 6, 144] Linear Code over GF(3) ConstructionX using [7] [6] and [5] [9]: [215, 6, 141] Linear Code over GF(3) Puncturing of [8] at { 5, 109, 125, 201 } [10]: [213, 6, 139] Linear Code over GF(3) Puncturing of [9] at { 214 .. 215 } last modified: 2004-07-27
Lb(213,6) = 139 is found by truncation of: Lb(215,6) = 141 Koh Ub(213,6) = 140 follows by a one-step Griesmer bound from: Ub(72,5) = 46 is found by considering truncation to: Ub(71,5) = 45 HW1
Koh: Axel Kohnert, email, 2006.
Notes
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