MinT - Information on Result #634939

Information on Result #634939

Linear OA(4⁶⁵, 75, F₄, 43) (dual of [75, 10, 44]-code), using concatenation of two codes based on

linear OA(16¹⁰, 15, F₁₆, 10) (dual of [15, 5, 11]-code or 15-arc in PG(9,16)), using
- discarding factors / shortening the dual code based on linear OA(16¹⁰, 16, F₁₆, 10) (dual of [16, 6, 11]-code or 16-arc in PG(9,16)), using
  - Reedâ€“Solomon code RS(6,16) [i]
linear OA(4³, 5, F₄, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,4) or 5-cap in PG(2,4)), using
- extended Reedâ€“Solomon code RS_e(2,4) [i]
- Simplex code S(2,4) [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(4⁶⁵, 75, F₄, 42) (dual of [75, 10, 43]-code)	[i]		Strength Reduction
2	Linear OA(4⁶⁵, 75, F₄, 41) (dual of [75, 10, 42]-code)	[i]		Strength Reduction
3	Linear OA(4⁶⁴, 74, F₄, 42) (dual of [74, 10, 43]-code)	[i]		Truncation
4	Linear OA(4⁶³, 73, F₄, 41) (dual of [73, 10, 42]-code)	[i]
5	Linear OA(4⁶², 72, F₄, 40) (dual of [72, 10, 41]-code)	[i]
6	Linear OA(4⁶¹, 71, F₄, 39) (dual of [71, 10, 40]-code)	[i]
7	Linear OA(4⁵⁹, 69, F₄, 37) (dual of [69, 10, 38]-code)	[i]
8	Linear OOA(4⁶⁵, 37, F₄, 2, 43) (dual of [(37, 2), 9, 44]-NRT-code)	[i]		OOA Folding
9	Linear OOA(4⁶⁵, 25, F₄, 3, 43) (dual of [(25, 3), 10, 44]-NRT-code)	[i]		OOA Folding