lower bound: | 123 |
upper bound: | 131 |
Construction of a linear code [207,11,123] over GF(3): [1]: [242, 11, 152] Cyclic Linear Code over GF(3) CyclicCode of length 242 with generating polynomial x^231 + 2*x^228 + 2*x^227 + x^226 + x^225 + 2*x^224 + 2*x^223 + x^221 + x^220 + x^218 + 2*x^216 + x^215 + x^213 + 2*x^212 + x^211 + x^210 + x^209 + x^208 + x^207 + 2*x^206 + x^205 + x^203 + 2*x^202 + x^200 + x^199 + 2*x^197 + 2*x^196 + 2*x^195 + 2*x^193 + 2*x^192 + 2*x^191 + 2*x^188 + x^186 + x^183 + x^182 + x^180 + x^179 + 2*x^177 + x^176 + x^175 + 2*x^174 + x^172 + 2*x^171 + 2*x^170 + 2*x^169 + x^168 + 2*x^164 + 2*x^161 + x^159 + 2*x^157 + x^156 + 2*x^155 + 2*x^154 + 2*x^153 + 2*x^152 + x^149 + x^148 + 2*x^147 + x^146 + 2*x^145 + x^142 + x^141 + 2*x^140 + 2*x^139 + 2*x^138 + 2*x^137 + 2*x^136 + 2*x^135 + x^133 + x^132 + x^131 + 2*x^130 + x^128 + x^126 + x^124 + x^121 + 2*x^118 + x^116 + 2*x^115 + x^114 + 2*x^113 + x^111 + 2*x^109 + x^108 + x^107 + 2*x^106 + x^105 + 2*x^104 + 2*x^103 + 2*x^101 + x^100 + 2*x^98 + x^97 + 2*x^96 + x^95 + x^94 + x^93 + x^90 + x^89 + x^88 + x^87 + 2*x^86 + x^85 + 2*x^83 + 2*x^82 + x^81 + 2*x^80 + x^75 + x^74 + x^72 + x^70 + 2*x^69 + 2*x^68 + x^64 + 2*x^60 + 2*x^59 + 2*x^58 + 2*x^56 + x^55 + x^53 + x^51 + x^49 + 2*x^48 + x^47 + 2*x^45 + 2*x^44 + x^43 + 2*x^41 + x^39 + 2*x^36 + 2*x^35 + x^30 + x^28 + 2*x^27 + 2*x^26 + 2*x^25 + 2*x^24 + x^22 + x^21 + 2*x^19 + x^18 + x^17 + x^16 + 2*x^15 + 2*x^14 + x^13 + x^12 + x^11 + x^8 + x^7 + 2*x^6 + 1 [2]: [207, 11, 123] Linear Code over GF(3) Puncturing of [1] at { 2, 3, 4, 6, 7, 8, 12, 14, 17, 19, 20, 24, 25, 37, 46, 49, 53, 55, 68, 73, 74, 89, 103, 116, 120, 124, 140, 142, 148, 156, 174, 178, 190, 220, 242 } last modified: 2006-09-29
Lb(207,11) = 123 MSY Ub(207,11) = 131 is found by considering shortening to: Ub(205,9) = 131 is found by considering truncation to: Ub(203,9) = 129 Gur
MSY: T. Maruta, M. Shinohara, F. Yamane, K. Tsuji, E. Takata, H. Miki & R. Fujiwara, New linear codes from cyclic or generalized cyclic codes by puncturing, to appear in Proc. 10th International Workshop on Algebraic and Combinatorial Coding Theory(ACCT-10) in Zvenigorod, Russia, 2006.
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