lower bound: | 100 |
upper bound: | 102 |
Construction of a linear code [140,6,100] over GF(4): [1]: [140, 6, 100] Quasicyclic of degree 4 Linear Code over GF(2^2) QuasiCyclicCode of length 140 with generating polynomials: w*x^34 + x^33 + x^32 + w^2*x^31 + w^2*x^30 + x^29 + x^28 + x^27 + w^2*x^26 + w^2*x^25 + x^24 + w*x^23 + x^22 + x^21 + x^20 + w^2*x^19 + w^2*x^18 + w*x^16 + w*x^15 + w*x^14 + w*x^13 + x^12 + x^11 + x^10 + w^2*x^9 + w^2*x^3 + w*x + w, w^2*x^34 + w*x^33 + w^2*x^32 + w*x^31 + w*x^28 + x^27 + x^26 + w*x^24 + x^23 + x^21 + x^19 + w^2*x^18 + w^2*x^17 + w^2*x^16 + x^14 + x^13 + w*x^12 + w*x^11 + w^2*x^9 + w*x^7 + w^2*x^6 + w*x^4 + w^2*x^3 + x^2, w^2*x^34 + x^33 + w^2*x^31 + w^2*x^30 + x^29 + x^28 + w^2*x^27 + w*x^26 + w*x^25 + w^2*x^24 + x^22 + x^20 + x^18 + x^17 + w^2*x^16 + w*x^15 + x^14 + w*x^12 + x^11 + w*x^9 + w^2*x^7 + x^6 + x^5 + w*x^4 + x^3 + w*x^2 + w*x + w^2, x^33 + x^32 + x^29 + w^2*x^28 + w^2*x^25 + x^24 + w*x^23 + w*x^22 + x^21 + x^19 + w^2*x^18 + w^2*x^17 + x^16 + w^2*x^12 + x^11 + w^2*x^10 + x^9 + w*x^8 + x^7 + w^2*x^5 + x^3 + w*x^2 + x + w^2 last modified: 2002-06-27
Lb(140,6) = 100 BKW Ub(140,6) = 102 follows by a one-step Griesmer bound from: Ub(37,5) = 25 follows by a one-step Griesmer bound from: Ub(11,4) = 6 is found by considering shortening to: Ub(10,3) = 6 GH
GH: P.P. Greenough & R. Hill, Optimal linear codes over GF(4), Discrete Math. 125 (1994) 187-199.
Notes
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