lower bound:  81 
upper bound:  88 
Construction of a linear code [196,17,81] over GF(2): [1]: [10, 1, 10] Cyclic Linear Code over GF(2) RepetitionCode of length 10 [2]: [195, 16, 88] Cyclic Linear Code over GF(2) CyclicCode of length 195 with generating polynomial x^179 + x^178 + x^175 + x^174 + x^169 + x^168 + x^165 + x^164 + x^162 + x^160 + x^157 + x^156 + x^154 + x^153 + x^149 + x^148 + x^143 + x^141 + x^134 + x^133 + x^131 + x^130 + x^129 + x^127 + x^126 + x^125 + x^123 + x^122 + x^119 + x^116 + x^113 + x^110 + x^109 + x^108 + x^102 + x^100 + x^99 + x^98 + x^90 + x^89 + x^88 + x^87 + x^85 + x^84 + x^83 + x^82 + x^81 + x^80 + x^79 + x^78 + x^75 + x^74 + x^72 + x^71 + x^66 + x^64 + x^62 + x^61 + x^60 + x^58 + x^57 + x^54 + x^51 + x^49 + x^43 + x^39 + x^38 + x^37 + x^33 + x^32 + x^30 + x^27 + x^26 + x^25 + x^22 + x^20 + x^17 + x^16 + x^15 + x^14 + x^11 + x^10 + x^9 + x^7 + x^6 + x^4 + x^3 + 1 [3]: [195, 18, 78] Cyclic Linear Code over GF(2) CyclicCode of length 195 with generating polynomial x^177 + x^175 + x^174 + x^173 + x^172 + x^170 + x^169 + x^166 + x^165 + x^162 + x^161 + x^160 + x^155 + x^153 + x^147 + x^145 + x^144 + x^142 + x^140 + x^138 + x^137 + x^135 + x^134 + x^131 + x^130 + x^129 + x^128 + x^127 + x^124 + x^122 + x^117 + x^116 + x^111 + x^110 + x^107 + x^105 + x^104 + x^102 + x^101 + x^100 + x^97 + x^95 + x^94 + x^92 + x^91 + x^89 + x^86 + x^84 + x^81 + x^78 + x^73 + x^71 + x^64 + x^63 + x^62 + x^59 + x^57 + x^52 + x^51 + x^47 + x^46 + x^44 + x^43 + x^37 + x^31 + x^29 + x^27 + x^26 + x^25 + x^24 + x^23 + x^21 + x^19 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^10 + x^7 + x^6 + x^5 + x^4 + x + 1 [4]: [195, 17, 78] Linear Code over GF(2) SubcodeBetweenCode of dimension 17 of [3] and [2] [5]: [205, 17, 88] Linear Code over GF(2) ConstructionX using [4] [2] and [1] [6]: [199, 17, 84] Linear Code over GF(2) Puncturing of [5] at { 1, 40, 79, 118, 157, 196 } [7]: [196, 17, 81] Linear Code over GF(2) Puncturing of [6] at { 197 .. 199 } last modified: 20040820
Lb(196,17) = 80 is found by taking a subcode of: Lb(196,18) = 80 is found by lengthening of: Lb(193,18) = 80 GW2 Ub(196,17) = 88 otherwise adding a parity check bit would contradict: Ub(197,17) = 89 BK
GW2: M. Grassl & G. White, New Codes from Chains of Quasicyclic Codes, ISIT 2005.
Notes
