lower bound: | 62 |
upper bound: | 67 |
Construction of a linear code [90,8,62] over GF(5): [1]: [124, 8, 93] Cyclic Linear Code over GF(5) CyclicCode of length 124 with generating polynomial x^116 + 3*x^115 + x^114 + 2*x^113 + 2*x^111 + x^110 + 2*x^109 + 3*x^106 + 4*x^104 + 4*x^103 + x^102 + 4*x^101 + 2*x^100 + 2*x^98 + 3*x^97 + 3*x^96 + 2*x^94 + x^91 + 3*x^90 + 2*x^89 + 3*x^88 + 3*x^87 + 4*x^86 + 4*x^85 + 3*x^84 + 3*x^83 + x^82 + 3*x^81 + 4*x^80 + 3*x^79 + 3*x^78 + 4*x^77 + 4*x^76 + 2*x^75 + x^74 + x^73 + 4*x^72 + 3*x^71 + 4*x^68 + x^66 + 4*x^65 + 4*x^64 + 4*x^63 + 2*x^62 + x^60 + x^59 + 2*x^58 + 2*x^57 + 4*x^56 + 2*x^54 + 3*x^53 + x^52 + 2*x^51 + x^50 + x^48 + x^45 + x^44 + 3*x^43 + x^42 + 4*x^41 + x^40 + 2*x^39 + 3*x^38 + x^37 + x^36 + 4*x^35 + x^34 + x^33 + 2*x^32 + 2*x^31 + 4*x^30 + x^29 + 2*x^28 + x^27 + 3*x^26 + 2*x^25 + 2*x^22 + 2*x^20 + 4*x^19 + 2*x^18 + 3*x^16 + 2*x^15 + x^14 + 3*x^13 + x^12 + 3*x^10 + x^7 + x^6 + 4*x^5 + x^3 + x^2 + x + 4 [2]: [90, 8, 62] Linear Code over GF(5) Puncturing of [1] at { 4, 5, 9, 10, 11, 15, 18, 20, 27, 31, 35, 36, 40, 44, 46, 50, 52, 54, 57, 64, 67, 69, 71, 73, 75, 76, 77, 83, 87, 93, 107, 109, 118, 120 } last modified: 2006-10-04
Lb(90,8) = 62 MSY Ub(90,8) = 67 follows by a one-step Griesmer bound from: Ub(22,7) = 13 follows by a one-step Griesmer bound from: Ub(8,6) = 2 is found by considering shortening to: Ub(7,5) = 2 is found by construction B: [consider deleting the (at most) 5 coordinates of a word in the dual]
Notes
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