lower bound: | 74 |
upper bound: | 75 |
Construction of a linear code [100,7,74] over GF(5): [1]: [124, 7, 94] Cyclic Linear Code over GF(5) CyclicCode of length 124 with generating polynomial x^117 + 4*x^115 + 4*x^113 + 4*x^112 + 3*x^110 + 4*x^108 + 4*x^107 + 2*x^106 + 2*x^105 + x^104 + 4*x^103 + 4*x^102 + 2*x^101 + 2*x^98 + x^97 + 3*x^96 + 2*x^95 + 4*x^93 + 2*x^92 + 3*x^91 + 3*x^90 + x^89 + x^88 + 4*x^87 + 3*x^86 + 4*x^85 + 3*x^84 + 2*x^83 + x^81 + 3*x^79 + 3*x^78 + 2*x^77 + 3*x^76 + 4*x^75 + 4*x^74 + 2*x^72 + x^71 + 4*x^70 + x^69 + 4*x^68 + 4*x^67 + x^66 + 4*x^65 + 4*x^64 + 4*x^62 + 3*x^61 + 2*x^59 + 4*x^58 + 2*x^57 + x^56 + 4*x^55 + 2*x^54 + 2*x^53 + 4*x^52 + 2*x^51 + 2*x^50 + x^49 + x^48 + 2*x^47 + 3*x^46 + 2*x^45 + 2*x^43 + x^41 + x^40 + 2*x^39 + 4*x^38 + 2*x^35 + 3*x^34 + 4*x^33 + 2*x^32 + x^31 + 2*x^29 + 2*x^26 + 2*x^24 + 4*x^23 + x^22 + 4*x^21 + 4*x^20 + 3*x^19 + 4*x^18 + 3*x^17 + x^15 + x^14 + 4*x^13 + 2*x^12 + 4*x^11 + 3*x^10 + 4*x^9 + 2*x^8 + x^6 + 4*x^5 + x^4 + 3*x + 1 [2]: [100, 7, 74] Linear Code over GF(5) Puncturing of [1] at { 12, 17, 19, 25, 28, 29, 43, 48, 50, 56, 59, 60, 74, 79, 81, 87, 90, 91, 105, 110, 112, 118, 121, 122 } last modified: 2006-10-04
Lb(100,7) = 74 MSY Ub(100,7) = 75 follows by a one-step Griesmer bound from: Ub(24,6) = 15 follows by a one-step Griesmer bound from: Ub(8,5) = 3 is found by considering shortening to: Ub(7,4) = 3 is found by construction B: [consider deleting the (at most) 4 coordinates of a word in the dual]
Notes
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