MinT - Information on Result #636849

Information on Result #636849

Linear OA(4¹⁷⁴, 225, F₄, 86) (dual of [225, 51, 87]-code), using concatenation of two codes based on

linear OA(64²⁸, 45, F₆₄, 28) (dual of [45, 17, 29]-code or 45-arc in PG(27,64)), using
- discarding factors / shortening the dual code based on linear OA(64²⁸, 64, F₆₄, 28) (dual of [64, 36, 29]-code or 64-arc in PG(27,64)), using
  - Reedâ€“Solomon code RS(36,64) [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.

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(4¹⁷⁴, 225, F₄, 85) (dual of [225, 51, 86]-code)	[i]		Strength Reduction
2	Linear OA(4¹⁷⁵, 226, F₄, 86) (dual of [226, 51, 87]-code)	[i]		Code Embedding in Larger Space
3	Linear OA(4¹⁷³, 224, F₄, 85) (dual of [224, 51, 86]-code)	[i]		Truncation
4	Linear OA(4¹⁷², 223, F₄, 84) (dual of [223, 51, 85]-code)	[i]		Truncation
5	Linear OOA(4¹⁷⁴, 112, F₄, 2, 86) (dual of [(112, 2), 50, 87]-NRT-code)	[i]		OOA Folding
6	Linear OOA(4¹⁷⁴, 75, F₄, 3, 86) (dual of [(75, 3), 51, 87]-NRT-code)	[i]		OOA Folding