MinT - Information on Result #636739

Information on Result #636739

Linear OA(4¹²⁶, 165, F₄, 62) (dual of [165, 39, 63]-code), using concatenation of two codes based on

linear OA(64²⁰, 33, F₆₄, 20) (dual of [33, 13, 21]-code or 33-arc in PG(19,64)), using
- discarding factors / shortening the dual code based on linear OA(64²⁰, 64, F₆₄, 20) (dual of [64, 44, 21]-code or 64-arc in PG(19,64)), using
  - Reedâ€“Solomon code RS(44,64) [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(4¹²⁶, 165, F₄, 61) (dual of [165, 39, 62]-code)	[i]		Strength Reduction
2	Linear OA(4¹²⁷, 166, F₄, 62) (dual of [166, 39, 63]-code)	[i]		Code Embedding in Larger Space
3	Linear OA(4¹²⁵, 164, F₄, 61) (dual of [164, 39, 62]-code)	[i]		Truncation
4	Linear OA(4¹²⁴, 163, F₄, 60) (dual of [163, 39, 61]-code)	[i]		Truncation
5	Linear OOA(4¹²⁶, 82, F₄, 2, 62) (dual of [(82, 2), 38, 63]-NRT-code)	[i]		OOA Folding
6	Linear OOA(4¹²⁶, 55, F₄, 3, 62) (dual of [(55, 3), 39, 63]-NRT-code)	[i]		OOA Folding