MinT - Information on Result #636831

Information on Result #636831

Linear OA(4¹⁹³, 280, F₄, 83) (dual of [280, 87, 84]-code), using concatenation of two codes based on

linear OA(64²⁷, 56, F₆₄, 27) (dual of [56, 29, 28]-code or 56-arc in PG(26,64)), using
- discarding factors / shortening the dual code based on linear OA(64²⁷, 64, F₆₄, 27) (dual of [64, 37, 28]-code or 64-arc in PG(26,64)), using
  - Reedâ€“Solomon code RS(37,64) [i]
linear OA(4², 5, F₄, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,4)), using
- extended Reedâ€“Solomon code RS_e(3,4) [i]
- Hamming code H(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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OA(4¹⁹³, 280, F₄, 82) (dual of [280, 87, 83]-code)	[i]		Strength Reduction
2	Linear OA(4¹⁹⁴, 281, F₄, 83) (dual of [281, 87, 84]-code)	[i]		Code Embedding in Larger Space
3	Linear OA(4¹⁹², 279, F₄, 82) (dual of [279, 87, 83]-code)	[i]		Truncation
4	Linear OA(4¹⁹¹, 278, F₄, 81) (dual of [278, 87, 82]-code)	[i]		Truncation
5	Linear OOA(4¹⁹³, 140, F₄, 2, 83) (dual of [(140, 2), 87, 84]-NRT-code)	[i]		OOA Folding
6	Linear OOA(4¹⁹³, 93, F₄, 3, 83) (dual of [(93, 3), 86, 84]-NRT-code)	[i]		OOA Folding