lower bound: | 85 |
upper bound: | 90 |
Construction of a linear code [200,17,85] over GF(2): [1]: [9, 1, 9] Cyclic Linear Code over GF(2) RepetitionCode of length 9 [2]: [195, 16, 88] Linear Code over GF(2) QuasiCyclicCode of length 195 stacked to height 3 with generating polynomials: x^13 + x^12 + x^11 + x^10 + x^6 + x^3 + x^2 + 1, x^12 + x^10 + x^6 + x^5 + x^2 + x, x^9 + x^6 + x^4 + x, x^10 + x^6 + x + 1, x^12 + x^10 + x^8 + x^6 + x^3 + x^2 + x + 1, x^13 + x^11 + x^9 + x^8 + x^6 + x^4, x^13 + x^12 + x^11 + x^9 + x^8 + x^6 + x^5 + x^4 + x^2 + 1, x^7 + x^6 + x^5 + x^2 + x + 1, x^12 + x^9 + x^7 + x^4, x^13 + x^12 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x + 1, x^13 + x^11 + x^9 + x^6 + x^5 + x^4 + x^3 + 1, x^11 + x^10 + x^7 + x^6 + x^2 + 1, x^12 + x^9 + x^8 + x^6 + x^4 + x^3 + x^2 + x, x^13 + x^10 + x^9 + x^7 + x^5 + x^4 + x^3 + x^2, x^13 + x^12 + x^11 + x^10 + x^6 + x^3 + x^2 + 1, x^12 + x^10 + x^6 + x^5 + x^2 + x, x^9 + x^6 + x^4 + x, x^10 + x^6 + x + 1, x^12 + x^10 + x^8 + x^6 + x^3 + x^2 + x + 1, x^13 + x^11 + x^9 + x^8 + x^6 + x^4, x^13 + x^12 + x^11 + x^9 + x^8 + x^6 + x^5 + x^4 + x^2 + 1, x^7 + x^6 + x^5 + x^2 + x + 1, x^12 + x^9 + x^7 + x^4, x^13 + x^12 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x + 1, x^13 + x^11 + x^9 + x^6 + x^5 + x^4 + x^3 + 1, x^11 + x^10 + x^7 + x^6 + x^2 + 1, x^12 + x^11 + x^8 + x^7 + x^3 + x, x^13 + x^10 + x^9 + x^7 + x^5 + x^4 + x^3 + x^2, x^13 + x^12 + x^11 + x^10 + x^6 + x^3 + x^2 + 1, x^12 + x^10 + x^6 + x^5 + x^2 + x, x^9 + x^6 + x^4 + x, x^10 + x^6 + x + 1, x^12 + x^10 + x^8 + x^6 + x^3 + x^2 + x + 1, x^13 + x^11 + x^9 + x^8 + x^6 + x^4, x^13 + x^12 + x^11 + x^9 + x^8 + x^6 + x^5 + x^4 + x^2 + 1, x^7 + x^6 + x^5 + x^2 + x + 1, x^12 + x^9 + x^7 + x^4, x^13 + x^12 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x + 1, x^13 + x^11 + x^9 + x^6 + x^5 + x^4 + x^3 + 1 [3]: [195, 17, 79] Linear Code over GF(2) QuasiCyclicCode of length 195 stacked to height 4 with generating polynomials: x^13 + x^12 + x^11 + x^10 + x^6 + x^3 + x^2 + 1, x^12 + x^10 + x^6 + x^5 + x^2 + x, x^9 + x^6 + x^4 + x, x^10 + x^6 + x + 1, x^12 + x^10 + x^8 + x^6 + x^3 + x^2 + x + 1, x^13 + x^11 + x^9 + x^8 + x^6 + x^4, x^13 + x^12 + x^11 + x^9 + x^8 + x^6 + x^5 + x^4 + x^2 + 1, x^7 + x^6 + x^5 + x^2 + x + 1, x^12 + x^9 + x^7 + x^4, x^13 + x^12 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x + 1, x^13 + x^11 + x^9 + x^6 + x^5 + x^4 + x^3 + 1, x^11 + x^10 + x^7 + x^6 + x^2 + 1, x^12 + x^9 + x^8 + x^6 + x^4 + x^3 + x^2 + x, x^13 + x^10 + x^9 + x^7 + x^5 + x^4 + x^3 + x^2, x^13 + x^12 + x^11 + x^10 + x^6 + x^3 + x^2 + 1, x^12 + x^10 + x^6 + x^5 + x^2 + x, x^9 + x^6 + x^4 + x, x^10 + x^6 + x + 1, x^12 + x^10 + x^8 + x^6 + x^3 + x^2 + x + 1, x^13 + x^11 + x^9 + x^8 + x^6 + x^4, x^13 + x^12 + x^11 + x^9 + x^8 + x^6 + x^5 + x^4 + x^2 + 1, x^7 + x^6 + x^5 + x^2 + x + 1, x^12 + x^9 + x^7 + x^4, x^13 + x^12 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x + 1, x^13 + x^11 + x^9 + x^6 + x^5 + x^4 + x^3 + 1, x^11 + x^10 + x^7 + x^6 + x^2 + 1, x^12 + x^11 + x^8 + x^7 + x^3 + x, x^13 + x^10 + x^9 + x^7 + x^5 + x^4 + x^3 + x^2, x^13 + x^12 + x^11 + x^10 + x^6 + x^3 + x^2 + 1, x^12 + x^10 + x^6 + x^5 + x^2 + x, x^9 + x^6 + x^4 + x, x^10 + x^6 + x + 1, x^12 + x^10 + x^8 + x^6 + x^3 + x^2 + x + 1, x^13 + x^11 + x^9 + x^8 + x^6 + x^4, x^13 + x^12 + x^11 + x^9 + x^8 + x^6 + x^5 + x^4 + x^2 + 1, x^7 + x^6 + x^5 + x^2 + x + 1, x^12 + x^9 + x^7 + x^4, x^13 + x^12 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x + 1, x^13 + x^11 + x^9 + x^6 + x^5 + x^4 + x^3 + 1, x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, 0, x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, 0, x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, 0, 0, x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1 [4]: [204, 17, 88] Linear Code over GF(2) ConstructionX using [3] [2] and [1] [5]: [201, 17, 86] Linear Code over GF(2) Puncturing of [4] at { 153, 158, 163 } [6]: [200, 17, 85] Linear Code over GF(2) Puncturing of [5] at { 201 } last modified: 2015-03-10
Lb(200,17) = 82 is found by shortening of: Lb(201,18) = 82 is found by adding a parity check bit to: Lb(200,18) = 81 Gra Ub(200,17) = 90 otherwise adding a parity check bit would contradict: Ub(201,17) = 91 BK
Gra:
Notes
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