lower bound:  71 
upper bound:  90 
Construction of a linear code [234,44,71] over GF(2): [1]: [255, 45, 87] Cyclic Linear Code over GF(2) CyclicCode of length 255 with generating polynomial x^210 + x^209 + x^207 + x^205 + x^199 + x^194 + x^192 + x^191 + x^190 + x^185 + x^183 + x^182 + x^180 + x^178 + x^175 + x^174 + x^173 + x^168 + x^167 + x^166 + x^162 + x^159 + x^157 + x^156 + x^153 + x^150 + x^144 + x^142 + x^141 + x^140 + x^137 + x^136 + x^133 + x^132 + x^131 + x^130 + x^129 + x^128 + x^127 + x^125 + x^121 + x^118 + x^117 + x^116 + x^115 + x^114 + x^108 + x^107 + x^105 + x^104 + x^103 + x^100 + x^99 + x^98 + x^97 + x^95 + x^94 + x^93 + x^85 + x^83 + x^80 + x^77 + x^76 + x^75 + x^71 + x^70 + x^69 + x^68 + x^67 + x^64 + x^61 + x^60 + x^59 + x^58 + x^57 + x^55 + x^54 + x^49 + x^48 + x^46 + x^45 + x^43 + x^37 + x^33 + x^32 + x^30 + x^29 + x^28 + x^27 + x^22 + x^20 + x^18 + x^14 + x^12 + x^9 + x^8 + x^6 + x^5 + 1 [2]: [254, 44, 87] Linear Code over GF(2) Shortening of [1] at 1 [3]: [234, 44, 71] Linear Code over GF(2) Puncturing of [2] at { 18, 46, 52, 57, 79, 84, 110, 112, 137, 155, 156, 165, 172, 183, 222, 224, 229, 239, 241, 249 } last modified: 20210830
Lb(234,44) = 68 is found by shortening of: Lb(236,46) = 68 is found by truncation of: Lb(240,46) = 72 is found by adding a parity check bit to: Lb(239,46) = 71 is found by construction B2: [shorten & puncture in a [255,47,85]code the (at most) 16 coordinates of a word in the dual] Ub(234,44) = 90 is found by considering shortening to: Ub(216,26) = 90 otherwise adding a parity check bit would contradict: Ub(217,26) = 91 BK
Notes
