MinT - Information on Result #636806

Information on Result #636806

Linear OA(4¹⁵⁹, 210, F₄, 77) (dual of [210, 51, 78]-code), using concatenation of two codes based on

linear OA(64²⁵, 42, F₆₄, 25) (dual of [42, 17, 26]-code or 42-arc in PG(24,64)), using
- discarding factors / shortening the dual code based on linear OA(64²⁵, 64, F₆₄, 25) (dual of [64, 39, 26]-code or 64-arc in PG(24,64)), using
  - Reedâ€“Solomon code RS(39,64) [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(4¹⁵⁹, 210, F₄, 76) (dual of [210, 51, 77]-code)	[i]		Strength Reduction
2	Linear OA(4¹⁶⁰, 211, F₄, 77) (dual of [211, 51, 78]-code)	[i]		Code Embedding in Larger Space
3	Linear OA(4¹⁵⁸, 209, F₄, 76) (dual of [209, 51, 77]-code)	[i]		Truncation
4	Linear OA(4¹⁵⁷, 208, F₄, 75) (dual of [208, 51, 76]-code)	[i]		Truncation
5	Linear OOA(4¹⁵⁹, 105, F₄, 2, 77) (dual of [(105, 2), 51, 78]-NRT-code)	[i]		OOA Folding
6	Linear OOA(4¹⁵⁹, 70, F₄, 3, 77) (dual of [(70, 3), 51, 78]-NRT-code)	[i]		OOA Folding