lower bound: | 118 |
upper bound: | 125 |
Construction of a linear code [198,10,118] 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^230 + 2*x^229 + 2*x^226 + 2*x^223 + x^222 + 2*x^221 + 2*x^220 + 2*x^219 + 2*x^217 + 2*x^215 + x^214 + 2*x^213 + 2*x^209 + x^207 + x^206 + 2*x^205 + 2*x^203 + x^201 + x^199 + 2*x^198 + x^197 + 2*x^194 + x^193 + 2*x^192 + 2*x^191 + x^190 + x^189 + x^188 + x^184 + x^183 + x^182 + 2*x^181 + 2*x^180 + x^179 + 2*x^176 + x^174 + 2*x^173 + 2*x^172 + x^171 + 2*x^170 + 2*x^169 + 2*x^168 + x^167 + x^166 + 2*x^165 + x^163 + x^162 + 2*x^161 + x^159 + x^157 + 2*x^156 + x^153 + 2*x^152 + 2*x^151 + 2*x^150 + 2*x^149 + 2*x^147 + x^146 + x^145 + x^143 + 2*x^140 + x^138 + x^137 + x^134 + 2*x^133 + 2*x^132 + x^131 + 2*x^130 + x^127 + 2*x^126 + 2*x^125 + x^124 + 2*x^123 + x^122 + x^121 + x^120 + 2*x^119 + x^118 + x^116 + x^115 + 2*x^111 + 2*x^109 + x^107 + x^105 + x^103 + 2*x^101 + x^100 + 2*x^99 + x^98 + 2*x^96 + 2*x^93 + 2*x^92 + x^91 + x^89 + 2*x^88 + 2*x^87 + x^86 + x^83 + 2*x^82 + 2*x^81 + 2*x^80 + x^79 + 2*x^78 + x^77 + 2*x^76 + 2*x^75 + 2*x^71 + x^70 + 2*x^69 + x^68 + x^67 + 2*x^66 + 2*x^64 + 2*x^62 + x^61 + 2*x^60 + 2*x^59 + x^58 + 2*x^57 + 2*x^55 + 2*x^54 + 2*x^53 + x^51 + 2*x^48 + x^47 + x^46 + x^45 + x^43 + 2*x^42 + 2*x^41 + 2*x^40 + 2*x^39 + x^37 + 2*x^36 + 2*x^35 + x^33 + 2*x^32 + x^31 + 2*x^29 + 2*x^28 + x^27 + 2*x^26 + 2*x^24 + 2*x^23 + 2*x^22 + 2*x^21 + 2*x^20 + 2*x^18 + x^16 + 2*x^15 + 2*x^14 + 2*x^12 + 2*x^11 + 2*x^10 + x^9 + x^8 + x^7 + 2*x^6 + x^2 + 1 [2]: [198, 10, 118] Linear Code over GF(3) Puncturing of [1] at { 1, 2, 3, 4, 5, 7, 8, 10, 15, 23, 25, 27, 28, 31, 34, 48, 68, 74, 77, 82, 90, 99, 104, 110, 121, 123, 143, 149, 155, 164, 168, 169, 170, 176, 177, 179, 183, 189, 196, 199, 221, 237, 240, 242 } last modified: 2006-09-01
Lb(198,10) = 118 MSY Ub(198,10) = 125 is found by considering shortening to: Ub(197,9) = 125 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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