MinT - Information on Result #636823

Information on Result #636823

Linear OA(4¹⁶⁰, 205, F₄, 80) (dual of [205, 45, 81]-code), using concatenation of two codes based on

linear OA(64²⁶, 41, F₆₄, 26) (dual of [41, 15, 27]-code or 41-arc in PG(25,64)), using
- discarding factors / shortening the dual code based on linear OA(64²⁶, 64, F₆₄, 26) (dual of [64, 38, 27]-code or 64-arc in PG(25,64)), using
  - Reedâ€“Solomon code RS(38,64) [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(4¹⁶⁰, 205, F₄, 79) (dual of [205, 45, 80]-code)	[i]		Strength Reduction
2	Linear OA(4¹⁶¹, 206, F₄, 80) (dual of [206, 45, 81]-code)	[i]		Code Embedding in Larger Space
3	Linear OA(4¹⁵⁹, 204, F₄, 79) (dual of [204, 45, 80]-code)	[i]		Truncation
4	Linear OA(4¹⁵⁸, 203, F₄, 78) (dual of [203, 45, 79]-code)	[i]		Truncation
5	Linear OOA(4¹⁶⁰, 102, F₄, 2, 80) (dual of [(102, 2), 44, 81]-NRT-code)	[i]		OOA Folding
6	Linear OOA(4¹⁶⁰, 68, F₄, 3, 80) (dual of [(68, 3), 44, 81]-NRT-code)	[i]		OOA Folding