lower bound: | 96 |
upper bound: | 98 |
Construction of a linear code [130,8,96] over GF(5): [1]: [31, 28, 3] "Hamming code (r = 3)" Linear Code over GF(5) 3-rd order HammingCode over GF( 5) [2]: [26, 23, 3] Linear Code over GF(5) Shortening of [1] at { 27 .. 31 } [3]: [6, 4, 3] Linear Code over GF(5) Construction B of [2] [4]: [124, 4, 99] Cyclic Linear Code over GF(5) CyclicCode of length 124 with generating polynomial x^120 + 2*x^117 + 3*x^116 + 4*x^114 + 2*x^113 + 4*x^112 + 3*x^111 + x^110 + 4*x^109 + 3*x^108 + x^107 + x^106 + 3*x^105 + x^104 + 4*x^102 + x^101 + 3*x^100 + 3*x^99 + 4*x^98 + 4*x^97 + 2*x^95 + 2*x^93 + 4*x^92 + x^91 + 4*x^90 + 4*x^89 + 4*x^88 + x^87 + 4*x^84 + 3*x^83 + 3*x^81 + 3*x^80 + 4*x^79 + x^78 + 2*x^76 + 4*x^75 + 3*x^74 + 4*x^73 + 4*x^72 + 3*x^71 + 2*x^70 + 3*x^68 + 3*x^67 + x^66 + x^65 + x^63 + 3*x^61 + 2*x^60 + 3*x^59 + x^58 + 3*x^57 + 2*x^56 + x^55 + 4*x^54 + 3*x^53 + 3*x^52 + x^51 + 3*x^50 + x^48 + 4*x^47 + 4*x^46 + 2*x^45 + x^44 + x^42 + 3*x^41 + 3*x^40 + 2*x^39 + 4*x^38 + 3*x^36 + 4*x^35 + 2*x^34 + x^33 + 2*x^32 + x^31 + 3*x^30 + 2*x^29 + 3*x^28 + 4*x^27 + 3*x^26 + 2*x^25 + 2*x^24 + 3*x^23 + 3*x^22 + 2*x^20 + 4*x^18 + 4*x^17 + x^16 + 3*x^15 + 4*x^13 + 4*x^12 + 4*x^11 + 3*x^10 + 3*x^7 + 4*x^6 + x^4 + 2*x^3 + 2*x^2 + 2*x + 2 [5]: [124, 8, 93] Cyclic Linear Code over GF(5) CyclicCode of length 124 with generating polynomial x^116 + 2*x^115 + 4*x^114 + 4*x^111 + 2*x^109 + 3*x^108 + 2*x^107 + 3*x^105 + x^102 + x^101 + 3*x^100 + x^99 + 3*x^98 + 4*x^97 + 2*x^96 + 4*x^95 + 3*x^94 + 3*x^93 + x^90 + 4*x^88 + 4*x^87 + 4*x^86 + 2*x^85 + x^84 + x^83 + 4*x^81 + 4*x^80 + 3*x^79 + x^78 + 3*x^77 + 2*x^76 + 4*x^75 + x^74 + 3*x^73 + 2*x^72 + x^71 + 2*x^70 + 4*x^69 + x^68 + 2*x^67 + 3*x^65 + x^64 + 4*x^63 + 4*x^62 + 2*x^60 + 3*x^59 + 4*x^58 + x^57 + 3*x^56 + 4*x^54 + 3*x^53 + 4*x^52 + 4*x^51 + 4*x^49 + 4*x^48 + 2*x^47 + 2*x^46 + 2*x^45 + 3*x^44 + 4*x^43 + x^42 + 3*x^41 + 3*x^40 + 4*x^39 + x^38 + x^37 + x^36 + 2*x^35 + 2*x^33 + 4*x^32 + x^31 + 4*x^30 + 3*x^29 + x^28 + x^26 + 4*x^23 + 3*x^22 + 3*x^21 + 3*x^20 + 2*x^19 + 3*x^18 + 2*x^17 + 2*x^16 + 3*x^15 + x^14 + 4*x^11 + 4*x^9 + 2*x^8 + x^7 + 3*x^5 + 4*x^2 + 4*x + 4 [6]: [130, 8, 96] Linear Code over GF(5) ConstructionX using [5] [4] and [3] last modified: 2008-05-17
Lb(130,8) = 96 X6a Ub(130,8) = 98 is found by considering shortening to: Ub(129,7) = 98 is found by considering truncation to: Ub(128,7) = 97 LP
X6a:
Notes
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