lower bound: | 79 |
upper bound: | 84 |
Construction of a linear code [188,17,79] over GF(2): [1]: [3, 1, 3] Cyclic Linear Code over GF(2) RepetitionCode of length 3 [2]: [186, 16, 80] Quasicyclic of degree 2 Linear Code over GF(2) QuasiCyclicCode of length 186 with generating polynomials: x^92 + x^90 + x^86 + x^85 + x^84 + x^82 + x^81 + x^80 + x^79 + x^78 + x^76 + x^71 + x^69 + x^66 + x^62 + x^60 + x^58 + x^55 + x^52 + x^51 + x^49 + x^48 + x^46 + x^44 + x^41 + x^40 + x^38 + x^37 + x^33 + x^32 + x^31 + x^29 + x^25 + x^23 + x^19 + x^16 + 1, x^92 + x^90 + x^88 + x^84 + x^80 + x^79 + x^78 + x^77 + x^74 + x^70 + x^69 + x^68 + x^66 + x^64 + x^62 + x^58 + x^57 + x^55 + x^53 + x^52 + x^49 + x^48 + x^47 + x^44 + x^41 + x^39 + x^38 + x^37 + x^34 + x^33 + x^29 + x^28 + x^27 + x^26 + x^24 + x^22 + x^21 + x^20 + x^18 + x^17 + x^16 + x^7 + x^6 + x^4 + x^3 [3]: [186, 17, 77] Quasicyclic of degree 2 Linear Code over GF(2) QuasiCyclicCode of length 186 stacked to height 2 with generating polynomials: x^77 + x^76 + x^74 + x^70 + x^69 + x^68 + x^66 + x^65 + x^64 + x^63 + x^62 + x^60 + x^55 + x^53 + x^50 + x^46 + x^44 + x^42 + x^39 + x^36 + x^35 + x^33 + x^32 + x^30 + x^28 + x^25 + x^24 + x^22 + x^21 + x^17 + x^16 + x^15 + x^13 + x^9 + x^7 + x^3 + 1, x^84 + x^83 + x^81 + x^80 + x^76 + x^74 + x^72 + x^68 + x^64 + x^63 + x^62 + x^61 + x^58 + x^54 + x^53 + x^52 + x^50 + x^48 + x^46 + x^42 + x^41 + x^39 + x^37 + x^36 + x^33 + x^32 + x^31 + x^28 + x^25 + x^23 + x^22 + x^21 + x^18 + x^17 + x^13 + x^12 + x^11 + x^10 + x^8 + x^6 + x^5 + x^4 + x^2 + x + 1, x^92 + x^91 + x^90 + x^89 + x^88 + x^87 + x^86 + x^85 + x^84 + x^83 + x^82 + x^81 + x^80 + x^79 + x^78 + x^77 + x^76 + x^75 + x^74 + x^73 + x^72 + x^71 + x^70 + x^69 + x^68 + x^67 + x^66 + x^65 + x^64 + x^63 + x^62 + x^61 + x^60 + x^59 + x^58 + x^57 + x^56 + x^55 + x^54 + x^53 + x^52 + x^51 + x^50 + x^49 + x^48 + x^47 + x^46 + x^45 + x^44 + x^43 + x^42 + x^41 + x^40 + x^39 + x^38 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + 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 [4]: [189, 17, 80] Linear Code over GF(2) ConstructionX using [3] [2] and [1] [5]: [188, 17, 79] Linear Code over GF(2) Puncturing of [4] at { 189 } last modified: 2014-03-28
Lb(188,17) = 78 is found by shortening of: Lb(189,18) = 78 is found by adding a parity check bit to: Lb(188,18) = 77 GW2 Ub(188,17) = 84 otherwise adding a parity check bit would contradict: Ub(189,17) = 85 BK
GW2: M. Grassl & G. White, New Codes from Chains of Quasi-cyclic Codes, ISIT 2005.
Notes
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