lower bound: | 52 |
upper bound: | 55 |
Construction of a linear code [75,7,52] over GF(5): [1]: [124, 7, 94] Cyclic Linear Code over GF(5) CyclicCode of length 124 with generating polynomial x^117 + x^116 + 4*x^115 + 2*x^114 + 2*x^113 + 3*x^112 + 3*x^111 + 2*x^110 + 2*x^109 + 3*x^107 + 2*x^106 + 4*x^105 + 2*x^104 + x^101 + 3*x^100 + 2*x^99 + x^97 + 2*x^96 + 2*x^95 + 3*x^94 + 4*x^92 + 4*x^91 + 4*x^88 + 2*x^87 + 2*x^86 + 2*x^85 + 4*x^84 + 4*x^83 + x^82 + 2*x^81 + 3*x^80 + x^79 + 3*x^78 + 3*x^77 + 4*x^76 + 3*x^75 + 3*x^74 + 3*x^72 + 3*x^71 + 4*x^69 + x^68 + x^67 + 3*x^65 + 2*x^64 + x^63 + 3*x^62 + x^61 + 3*x^60 + 3*x^59 + x^58 + x^57 + x^56 + 2*x^55 + 4*x^53 + 2*x^52 + 3*x^51 + 4*x^50 + x^49 + 4*x^48 + 4*x^46 + 2*x^45 + x^44 + 4*x^43 + 2*x^40 + x^38 + 2*x^37 + 3*x^34 + 3*x^33 + x^32 + x^31 + 3*x^29 + 2*x^28 + 4*x^27 + 2*x^25 + 2*x^23 + 3*x^22 + 2*x^21 + 4*x^20 + x^19 + 3*x^18 + 3*x^17 + 3*x^15 + x^14 + 4*x^13 + 4*x^12 + 3*x^11 + 2*x^10 + 4*x^8 + 2*x^7 + 4*x^5 + 4*x^4 + 2*x^3 + 3*x^2 + 1 [2]: [75, 7, 52] Linear Code over GF(5) Puncturing of [1] at { 2, 3, 4, 5, 9, 11, 13, 17, 18, 20, 22, 25, 29, 31, 33, 34, 35, 36, 37, 41, 45, 48, 49, 50, 51, 52, 56, 60, 66, 67, 72, 76, 79, 80, 82, 87, 89, 91, 95, 96, 97, 103, 107, 110, 111, 113, 118, 122, 124 } last modified: 2006-10-04
Lb(75,7) = 52 MSY Ub(75,7) = 55 follows by a one-step Griesmer bound from: Ub(19,6) = 11 follows by a one-step Griesmer bound from: 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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