MinT - Information on Result #637290

Information on Result #637290

Linear OA(4¹⁴⁷, 168, F₄, 87) (dual of [168, 21, 88]-code), using concatenation of two codes based on

linear OA(64²¹, 28, F₆₄, 21) (dual of [28, 7, 22]-code or 28-arc in PG(20,64)), using
- discarding factors / shortening the dual code based on linear OA(64²¹, 64, F₆₄, 21) (dual of [64, 43, 22]-code or 64-arc in PG(20,64)), using
  - Reedâ€“Solomon code RS(43,64) [i]
linear OA(4³, 6, F₄, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,4) or 6-cap in PG(2,4)), using
- hyperoval in PG(2,Â 4) [i]
- the Hexacode [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(4¹⁴⁷, 168, F₄, 86) (dual of [168, 21, 87]-code)	[i]		Strength Reduction
2	Linear OA(4¹⁴⁷, 168, F₄, 85) (dual of [168, 21, 86]-code)	[i]		Strength Reduction
3	Linear OA(4¹⁴⁸, 169, F₄, 87) (dual of [169, 21, 88]-code)	[i]		Code Embedding in Larger Space
4	Linear OA(4¹⁴⁶, 167, F₄, 86) (dual of [167, 21, 87]-code)	[i]		Truncation
5	Linear OA(4¹⁴⁵, 166, F₄, 85) (dual of [166, 21, 86]-code)	[i]
6	Linear OA(4¹⁴⁴, 165, F₄, 84) (dual of [165, 21, 85]-code)	[i]
7	Linear OOA(4¹⁴⁷, 84, F₄, 2, 87) (dual of [(84, 2), 21, 88]-NRT-code)	[i]		OOA Folding
8	Linear OOA(4¹⁴⁷, 56, F₄, 3, 87) (dual of [(56, 3), 21, 88]-NRT-code)	[i]		OOA Folding