MinT - Information on Result #636762

Information on Result #636762

Linear OA(4¹⁴⁶, 200, F₄, 68) (dual of [200, 54, 69]-code), using concatenation of two codes based on

linear OA(64²², 40, F₆₄, 22) (dual of [40, 18, 23]-code or 40-arc in PG(21,64)), using
- discarding factors / shortening the dual code based on linear OA(64²², 64, F₆₄, 22) (dual of [64, 42, 23]-code or 64-arc in PG(21,64)), using
  - Reedâ€“Solomon code RS(42,64) [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(4¹⁴⁶, 200, F₄, 67) (dual of [200, 54, 68]-code)	[i]		Strength Reduction
2	Linear OA(4¹⁴⁷, 201, F₄, 68) (dual of [201, 54, 69]-code)	[i]		Code Embedding in Larger Space
3	Linear OA(4¹⁴⁵, 199, F₄, 67) (dual of [199, 54, 68]-code)	[i]		Truncation
4	Linear OA(4¹⁴⁴, 198, F₄, 66) (dual of [198, 54, 67]-code)	[i]		Truncation
5	Linear OOA(4¹⁴⁶, 100, F₄, 2, 68) (dual of [(100, 2), 54, 69]-NRT-code)	[i]		OOA Folding
6	Linear OOA(4¹⁴⁶, 66, F₄, 3, 68) (dual of [(66, 3), 52, 69]-NRT-code)	[i]		OOA Folding