lower bound:  33 
upper bound:  35 
Construction of a linear code [50,7,33] over GF(5): [1]: [1, 1, 1] Cyclic Linear Code over GF(5) RepetitionCode of length 1 [2]: [48, 6, 32] Quasicyclic of degree 4 Linear Code over GF(5) QuasiCyclicCode of length 48 with generating polynomials: 4*x^11 + 3*x^10 + 2*x^9 + x^8 + x^7 + 3*x^6 + 1, 3*x^11 + 2*x^9 + 2*x^8 + 3*x^6 + x^4 + x^3 + 2*x^2 + 1, 3*x^11 + 2*x^10 + 3*x^8 + 4*x^7 + x^6 + x^5 + 3*x^3 + 3*x^2 + x + 4, x^11 + 2*x^10 + x^9 + 2*x^8 + x^7 + 3*x^6 + x^5 + x^3 + 3*x^2 + 3*x + 2 [3]: [48, 6, 32] Quasicyclic of degree 4 Linear Code over GF(5) QuasiCyclicCode of length 48 with generating polynomials: x^11 + x^10 + 3*x^9 + x^7 + 3*x^6 + x^2, 3*x^11 + x^8 + 4*x^6 + 2*x^5 + x^4 + 4*x^3 + 4*x^2 + x, 2*x^11 + 3*x^10 + 3*x^9 + x^8 + 2*x^6 + x^5 + x^3 + 2*x^2 + 3*x + 2, x^11 + 3*x^10 + 2*x^9 + x^8 + 2*x^7 + 4*x^6 + 4*x^5 + 3*x^4 + 2*x^3 + 4*x^2 + 4*x [4]: [48, 7, 31] Quasicyclic of degree 4 Linear Code over GF(5) QuasiCyclicCode of length 48 with generating polynomials: x^10 + x^9 + 2*x^7 + x^5, x^11 + 3*x^10 + 4*x^9 + 3*x^8 + 3*x^7 + 3*x^6 + x^5 + x^2 + 3*x + 3, 4*x^10 + x^9 + 4*x^8 + 3*x^7 + 4*x^6 + 2*x^5 + x^3 + 2*x^2 + 2*x + 2, 4*x^11 + x^9 + 4*x^8 + 4*x^7 + x^5 + x^3 + 2*x^2 + 3 [5]: [50, 7, 33] Linear Code over GF(5) ConstructionXX using [4] [3] [2] [1] and [1] last modified: 20080528
Lb(50,7) = 32 is found by shortening of: Lb(51,8) = 32 MST Ub(50,7) = 35 follows by a onestep Griesmer bound from: Ub(14,6) = 7 is found by considering shortening to: Ub(13,5) = 7 is found by considering truncation to: Ub(12,5) = 6 DL
MST: T. Maruta, M. Shinohara & M. Takenaka, Constructing linear codes from some orbits of projectivities, to appear in Discr. Math.
Notes
