lower bound: | 78 |
upper bound: | 80 |
Construction of a linear code [172,12,78] over GF(2): [1]: [4, 3, 2] Cyclic Linear Code over GF(2) Dual of the RepetitionCode of length 4 [2]: [168, 9, 80] Quasicyclic of degree 8 Linear Code over GF(2) QuasiCyclicCode of length 168 with generating polynomials: x^18 + x^15 + x^9 + 1, x^18 + x^15 + x^14 + x^13 + x^11 + x^10 + x^9 + x^8 + x^7 + x^2 + x + 1, x^18 + x^15 + x^13 + x^10 + x^9 + x^7 + x + 1, x^18 + x^16 + x^15 + x^12 + x^7 + x^6 + x^4 + x, x^20 + x^18 + x^17 + x^16 + x^15 + x^13 + x^12 + x^11 + x^10 + x^6 + x^4 + x^2, x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^2 + x + 1, x^20 + x^19 + x^18 + x^17 + x^15 + x^11 + x^10 + x^9 + x^7 + x^4 + x^2 + 1, x^20 + x^17 + x^16 + x^15 + x^14 + x^13 + x^10 + x^8 + x^6 + x^4 + x^3 + 1 [3]: [168, 12, 76] Quasicyclic of degree 8 Linear Code over GF(2) QuasiCyclicCode of length 168 with generating polynomials: x^15 + x^12 + 1, x^20 + x^18 + x^17 + x^13 + x^11 + x^9 + x^7 + x^6 + x^4 + x^3 + x^2, x^19 + x^18 + x^16 + x^10 + x^9 + x^6 + x^3 + x, x^20 + x^18 + x^17 + x^16 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^5 + x^4 + x^2, x^20 + x^16 + x^15 + x^11 + x^10 + x^8 + x^7 + x^6 + x^5 + x^3 + 1, x^14 + x^13 + x^12 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3, x^20 + x^15 + x^12 + x^11 + x^10 + x^8 + x^5 + x^4 + x + 1, x^20 + x^19 + x^18 + x^14 + x^13 + x^11 + x^6 + x^4 + x + 1 [4]: [172, 12, 78] Linear Code over GF(2) ConstructionX using [3] [2] and [1] last modified: 2003-04-02
Lb(172,12) = 78 GW2 Ub(172,12) = 80 follows by a one-step Griesmer bound from: Ub(91,11) = 40 follows by a one-step Griesmer bound from: Ub(50,10) = 20 is found by considering shortening to: Ub(49,9) = 20 Ja
Ja: D.B. Jaffe, Binary linear codes: new results on nonexistence, 1996, code.ps.gz.
Notes
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