MinT - Information on Result #638033

Information on Result #638033

Linear OA(5⁸⁶, 100, F₅, 56) (dual of [100, 14, 57]-code), using concatenation of two codes based on

linear OA(25¹⁸, 25, F₂₅, 18) (dual of [25, 7, 19]-code or 25-arc in PG(17,25)), using
- Reedâ€“Solomon code RS(7,25) [i]
linear OA(5², 4, F₅, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,5)), using
- discarding factors / shortening the dual code based on linear OA(5², 5, F₅, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,5)), using
  - Reedâ€“Solomon code RS(3,5) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OA(5⁸⁶, 100, F₅, 55) (dual of [100, 14, 56]-code)	[i]		Strength Reduction
2	Linear OA(5⁸⁵, 99, F₅, 55) (dual of [99, 14, 56]-code)	[i]		Truncation
3	Linear OA(5⁸⁴, 98, F₅, 54) (dual of [98, 14, 55]-code)	[i]
4	Linear OA(5⁸³, 97, F₅, 53) (dual of [97, 14, 54]-code)	[i]
5	Linear OA(5⁸¹, 95, F₅, 51) (dual of [95, 14, 52]-code)	[i]
6	Linear OOA(5⁸⁶, 50, F₅, 2, 56) (dual of [(50, 2), 14, 57]-NRT-code)	[i]		OOA Folding
7	Linear OOA(5⁸⁶, 33, F₅, 3, 56) (dual of [(33, 3), 13, 57]-NRT-code)	[i]		OOA Folding