lower bound: | 131 |
upper bound: | 137 |
Construction of a linear code [216,10,131] over GF(3): [1]: [242, 10, 153] Cyclic Linear Code over GF(3) CyclicCode of length 242 with generating polynomial x^232 + x^231 + 2*x^229 + 2*x^228 + 2*x^227 + x^226 + x^223 + x^220 + 2*x^217 + 2*x^216 + x^214 + x^213 + 2*x^212 + x^211 + 2*x^210 + 2*x^206 + 2*x^205 + x^204 + x^203 + 2*x^202 + 2*x^201 + x^200 + 2*x^195 + 2*x^193 + x^192 + 2*x^191 + 2*x^189 + x^188 + x^187 + 2*x^184 + x^183 + x^182 + 2*x^181 + 2*x^178 + 2*x^177 + x^176 + 2*x^175 + 2*x^172 + 2*x^171 + 2*x^169 + 2*x^168 + x^165 + 2*x^164 + x^163 + 2*x^162 + x^160 + 2*x^159 + 2*x^158 + 2*x^157 + 2*x^155 + x^154 + 2*x^152 + x^151 + 2*x^149 + 2*x^147 + 2*x^146 + x^144 + 2*x^143 + x^140 + 2*x^139 + 2*x^138 + x^137 + x^135 + x^134 + x^132 + x^131 + 2*x^129 + x^127 + x^126 + x^124 + x^123 + 2*x^122 + 2*x^121 + 2*x^119 + 2*x^118 + x^117 + 2*x^116 + 2*x^115 + 2*x^113 + x^112 + x^111 + 2*x^110 + 2*x^109 + x^108 + x^107 + 2*x^105 + 2*x^100 + x^99 + 2*x^98 + x^97 + x^96 + 2*x^94 + 2*x^92 + x^91 + 2*x^90 + 2*x^89 + 2*x^88 + x^87 + 2*x^86 + x^85 + x^84 + 2*x^82 + 2*x^81 + 2*x^80 + x^79 + 2*x^78 + 2*x^77 + x^74 + x^71 + x^70 + x^69 + 2*x^65 + x^62 + x^61 + x^59 + 2*x^58 + 2*x^57 + x^55 + x^53 + x^52 + x^51 + 2*x^48 + 2*x^46 + 2*x^45 + x^44 + 2*x^42 + 2*x^41 + x^40 + 2*x^39 + 2*x^38 + x^37 + x^34 + 2*x^32 + x^31 + 2*x^28 + 2*x^26 + x^23 + 2*x^22 + x^21 + 2*x^20 + x^19 + 2*x^18 + 2*x^16 + x^15 + x^14 + 2*x^13 + x^11 + x^9 + x^8 + x^4 + 2*x^3 + 2*x + 1 [2]: [216, 10, 131] Linear Code over GF(3) Puncturing of [1] at { 3, 8, 10, 15, 24, 25, 43, 62, 69, 79, 101, 118, 121, 128, 133, 146, 151, 152, 175, 176, 183, 193, 198, 211, 225, 242 } last modified: 2006-09-01
Lb(216,10) = 131 MSY Ub(216,10) = 137 is found by considering shortening to: Ub(215,9) = 137 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.
Notes
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