lower bound: | 134 |
upper bound: | 140 |
Construction of a linear code [219,10,134] over GF(3): [1]: [220, 10, 135] Quasicyclic of degree 10 Linear Code over GF(3) QuasiCyclicCode of length 220 with generating polynomials: x^21 + x^19 + x^18 + 2*x^15 + x^14 + x^13 + 2*x^12 + 2*x^10 + x^3, 2*x^19 + x^18 + 2*x^16 + 2*x^15 + x^13 + 2*x^9 + x^8 + 2*x^7 + x^5 + x^3 + x + 2, x^21 + 2*x^20 + 2*x^19 + 2*x^17 + 2*x^16 + x^15 + 2*x^14 + 2*x^13 + x^12 + x^11 + 2*x^6 + 2*x^5 + x^4 + x^3 + 2*x^2, 2*x^20 + 2*x^18 + 2*x^17 + 2*x^16 + x^14 + 2*x^12 + 2*x^11 + x^10 + 2*x^9 + 2*x^8 + 2*x^7 + 2*x^6 + 2*x^4 + x + 2, 2*x^21 + 2*x^20 + 2*x^19 + x^16 + x^15 + 2*x^14 + x^12 + 2*x^11 + 2*x^10 + x^9 + x^5 + x^3 + 2*x^2 + 2*x + 2, 2*x^21 + x^19 + 2*x^18 + 2*x^16 + x^14 + x^12 + x^11 + x^10 + x^9 + x^7 + x^6 + 2*x^5 + x^4 + 2*x^3 + 2*x, 2*x^21 + x^20 + x^18 + x^16 + x^15 + x^14 + x^13 + x^12 + 2*x^9 + 2*x^8 + x^6 + 2*x^5 + 2*x^4 + 2*x^2 + x, 2*x^19 + x^16 + 2*x^12 + x^11 + x^9 + x^7 + x^5 + x^4 + 2, x^20 + 2*x^19 + 2*x^18 + 2*x^17 + x^16 + 2*x^15 + 2*x^14 + x^13 + 2*x^12 + 2*x^10 + x^9 + x^8 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + x^2 + 2, x^21 + 2*x^20 + x^19 + x^18 + 2*x^17 + 2*x^15 + 2*x^13 + x^12 + x^11 + 2*x^9 + 2*x^7 + x^5 + x^3 + x^2 + 1 [2]: [219, 10, 134] Linear Code over GF(3) Puncturing of [1] at { 220 } last modified: 2009-12-14
Lb(219,10) = 133 is found by truncation of: Lb(220,10) = 134 MSY Ub(219,10) = 140 is found by considering shortening to: Ub(218,9) = 140 is found by considering truncation 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.
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