lower bound: | 50 |
upper bound: | 52 |
Construction of a linear code [70,6,50] over GF(5): [1]: [12, 7, 5] Linear Code over GF(5) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 4, 0, 1, 3, 2 ] [ 0, 1, 0, 0, 0, 0, 0, 1, 3, 0, 4, 2 ] [ 0, 0, 1, 0, 0, 0, 0, 2, 3, 2, 3, 0 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 3, 4, 2, 1 ] [ 0, 0, 0, 0, 1, 0, 0, 1, 4, 3, 0, 2 ] [ 0, 0, 0, 0, 0, 1, 0, 4, 3, 1, 4, 3 ] [ 0, 0, 0, 0, 0, 0, 1, 2, 4, 2, 0, 1 ] [2]: [8, 3, 5] Linear Code over GF(5) Shortening of [1] at { 9 .. 12 } [3]: [62, 3, 50] Quasicyclic of degree 2 Linear Code over GF(5) QuasiCyclicCode of length 62 with generating polynomials: 4*x^30 + 3*x^29 + x^28 + 4*x^27 + x^26 + 3*x^25 + 3*x^24 + 4*x^23 + x^21 + 3*x^20 + 4*x^19 + 3*x^18 + 3*x^17 + 2*x^16 + 2*x^15 + x^13 + x^12 + x^11 + 2*x^10 + x^9 + 4*x^8 + 4*x^6 + 3*x^4 + x^3 + 1, 2*x^30 + 3*x^29 + x^28 + 2*x^27 + 3*x^26 + 2*x^25 + x^24 + x^23 + 3*x^22 + 2*x^20 + x^19 + 3*x^18 + x^17 + x^16 + 4*x^15 + 4*x^14 + 2*x^12 + 2*x^11 + 2*x^10 + 4*x^9 + 2*x^8 + 3*x^7 + 3*x^5 + x^3 + 2*x^2 [4]: [62, 6, 45] Quasicyclic of degree 2 Linear Code over GF(5) QuasiCyclicCode of length 62 with generating polynomials: 4*x^29 + x^28 + 4*x^27 + 3*x^25 + 2*x^23 + 3*x^21 + 3*x^20 + 4*x^18 + x^16 + 2*x^15 + 3*x^14 + 2*x^13 + 3*x^12 + 4*x^11 + x^10 + 4*x^9 + 3*x^8 + 3*x^7 + 4*x^6 + 1, 2*x^30 + x^29 + 3*x^28 + 3*x^27 + 3*x^25 + 2*x^24 + x^23 + 4*x^22 + 2*x^21 + 4*x^20 + x^19 + x^17 + 3*x^16 + 3*x^15 + x^14 + 2*x^13 + 3*x^12 + 3*x^11 + 3*x^7 + 3*x^6 + 4*x^5 + 3*x^3 + 4*x^2 + 2*x + 4 [5]: [70, 6, 50] Linear Code over GF(5) ConstructionX using [4] [3] and [2] last modified: 2003-08-05
Lb(70,6) = 50 DaH Ub(70,6) = 52 follows by a one-step Griesmer bound from: Ub(17,5) = 10 is found by construction B: [consider deleting the (at most) 4 coordinates of a word in the dual]
Notes
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