MinT - Information on Result #636805

Information on Result #636805

Linear OA(4¹⁶¹, 215, F₄, 77) (dual of [215, 54, 78]-code), using concatenation of two codes based on

linear OA(64²⁵, 43, F₆₄, 25) (dual of [43, 18, 26]-code or 43-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(4¹⁶¹, 215, F₄, 76) (dual of [215, 54, 77]-code)	[i]		Strength Reduction
2	Linear OA(4¹⁶², 216, F₄, 77) (dual of [216, 54, 78]-code)	[i]		Code Embedding in Larger Space
3	Linear OA(4¹⁶⁰, 214, F₄, 76) (dual of [214, 54, 77]-code)	[i]		Truncation
4	Linear OA(4¹⁵⁹, 213, F₄, 75) (dual of [213, 54, 76]-code)	[i]		Truncation
5	Linear OOA(4¹⁶¹, 107, F₄, 2, 77) (dual of [(107, 2), 53, 78]-NRT-code)	[i]		OOA Folding
6	Linear OOA(4¹⁶¹, 71, F₄, 3, 77) (dual of [(71, 3), 52, 78]-NRT-code)	[i]		OOA Folding