lower bound: | 68 |
upper bound: | 72 |
Construction of a linear code [160,15,68] over GF(2): [1]: [24, 12, 8] Linear Code over GF(2) Extend the QRCode over GF(2)of length 23 [2]: [19, 7, 8] Linear Code over GF(2) Shortening of [1] at { 20 .. 24 } [3]: [4, 1, 4] Cyclic Linear Code over GF(2) RepetitionCode of length 4 [4]: [4, 3, 2] Cyclic Linear Code over GF(2) Dual of the RepetitionCode of length 4 [5]: [8, 4, 4] Quasicyclic of degree 2 Linear Code over GF(2) PlotkinSum of [4] and [3] [6]: [8, 7, 2] Cyclic Linear Code over GF(2) Dual of the RepetitionCode of length 8 [7]: [16, 11, 4] Linear Code over GF(2) PlotkinSum of [6] and [5] [8]: [12, 7, 4] Linear Code over GF(2) Shortening of [7] at { 13 .. 16 } [9]: [127, 8, 63] Cyclic Linear Code over GF(2) CyclicCode of length 127 with generating polynomial x^119 + x^118 + x^112 + x^109 + x^105 + x^104 + x^103 + x^102 + x^101 + x^100 + x^98 + x^96 + x^95 + x^94 + x^93 + x^90 + x^87 + x^86 + x^84 + x^83 + x^82 + x^81 + x^80 + x^75 + x^74 + x^73 + x^71 + x^68 + x^66 + x^63 + x^62 + x^61 + x^60 + x^58 + x^57 + x^56 + x^54 + x^53 + x^49 + x^44 + x^42 + x^41 + x^40 + x^37 + x^36 + x^33 + x^31 + x^30 + x^27 + x^26 + x^25 + x^21 + x^20 + x^18 + x^16 + x^14 + x^10 + x^8 + x^6 + x^5 + x^3 + x^2 + 1 [10]: [127, 8, 63] Cyclic Linear Code over GF(2) CyclicCode of length 127 with generating polynomial x^119 + x^118 + x^116 + x^115 + x^114 + x^113 + x^112 + x^111 + x^109 + x^106 + x^105 + x^104 + x^103 + x^102 + x^98 + x^96 + x^95 + x^94 + x^93 + x^91 + x^90 + x^86 + x^85 + x^84 + x^81 + x^79 + x^78 + x^76 + x^75 + x^73 + x^69 + x^66 + x^62 + x^61 + x^58 + x^55 + x^54 + x^52 + x^50 + x^47 + x^45 + x^39 + x^34 + x^33 + x^32 + x^31 + x^28 + x^27 + x^26 + x^24 + x^23 + x^22 + x^20 + x^18 + x^17 + x^14 + x^13 + x^8 + x^6 + x^4 + x^2 + x + 1 [11]: [127, 15, 55] Cyclic Linear Code over GF(2) CyclicCode of length 127 with generating polynomial x^112 + x^111 + x^110 + x^108 + x^105 + x^97 + x^96 + x^94 + x^93 + x^91 + x^90 + x^88 + x^85 + x^83 + x^82 + x^81 + x^80 + x^77 + x^76 + x^75 + x^73 + x^67 + x^65 + x^62 + x^56 + x^52 + x^51 + x^46 + x^45 + x^42 + x^41 + x^40 + x^39 + x^35 + x^33 + x^28 + x^26 + x^25 + x^24 + x^23 + x^22 + x^18 + x^17 + x^15 + x^14 + x^13 + x^11 + x^10 + x^9 + x^8 + x^7 + x^5 + x^4 + x^2 + 1 [12]: [158, 15, 67] Linear Code over GF(2) ConstructionXX using [11] [10] [9] [8] and [2] [13]: [159, 15, 68] Linear Code over GF(2) ExtendCode [12] by 1 [14]: [160, 15, 68] Linear Code over GF(2) ExtendCode [13] by 1 last modified: 2001-01-30
Lb(160,15) = 68 is found by adding a parity check bit to: Lb(159,15) = 67 XX Ub(160,15) = 72 follows by a one-step Griesmer bound from: Ub(87,14) = 36 is found by considering shortening to: Ub(86,13) = 36 Ja
XX:
Notes
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