lower bound:  47 
upper bound:  52 
Construction of a linear code [73,9,47] over GF(5): [1]: [1, 1, 1] Cyclic Linear Code over GF(5) RepetitionCode of length 1 [2]: [72, 8, 47] Quasicyclic of degree 3 Linear Code over GF(5) QuasiCyclicCode of length 72 with generating polynomials: 2*x^22 + x^21 + 4*x^20 + 2*x^19 + 2*x^18 + 2*x^17 + 3*x^16 + 2*x^15 + 4*x^13 + 2*x^12 + 3*x^9 + 2*x^8 + 1, 3*x^23 + 4*x^22 + 4*x^21 + 2*x^20 + 3*x^19 + x^18 + x^16 + x^14 + x^13 + 3*x^11 + 2*x^10 + 2*x^9 + x^8 + 2*x^7 + 4*x^6 + 3*x^5 + x^4 + 4*x^3 + x^2 + x + 1, 4*x^20 + x^19 + 4*x^18 + 3*x^17 + x^16 + 2*x^15 + 2*x^13 + 3*x^12 + x^11 + 3*x^10 + 3*x^9 + 2*x^8 + 4*x^5 + 3*x^2 + 4 [3]: [72, 9, 46] Quasicyclic of degree 3 Linear Code over GF(5) QuasiCyclicCode of length 72 with generating polynomials: 2*x^23 + x^22 + x^20 + x^18 + x^17 + 3*x^16 + 4*x^15 + x^14 + 3*x^13 + 2*x^12 + x^11 + 2*x^10 + 2*x^9 + x^6, 2*x^23 + x^22 + 3*x^20 + 4*x^19 + 4*x^18 + 4*x^17 + 2*x^16 + 2*x^14 + 4*x^12 + 4*x^11 + 3*x^10 + x^9 + 2*x^8 + 3*x^7 + x^5 + 4*x^4 + 2*x^3 + x^2 + x + 2, 3*x^22 + 2*x^21 + 4*x^20 + x^19 + 2*x^18 + 3*x^16 + 3*x^14 + 4*x^13 + x^10 + 2*x^9 + 2*x^7 + 3*x^5 + 4*x^4 + x^3 + 3*x^2 + 2*x [4]: [73, 9, 47] Linear Code over GF(5) ConstructionX using [3] [2] and [1] last modified: 20210825
Lb(73,9) = 46 is found by shortening of: Lb(74,10) = 46 is found by truncation of: Lb(78,10) = 50 Da Ub(73,9) = 52 follows by a onestep Griesmer bound from: Ub(20,8) = 10 follows by a onestep Griesmer bound from: Ub(9,7) = 2 is found by considering shortening to: Ub(7,5) = 2 is found by construction B: [consider deleting the (at most) 5 coordinates of a word in the dual]
Notes
