MinT - Information on Result #2202554

Information on Result #2202554

Linear OA(4¹⁴⁷, 168, F₄, 86) (dual of [168, 21, 87]-code), using strength reduction based on linear OA(4¹⁴⁷, 168, F₄, 87) (dual of [168, 21, 88]-code), using

concatenation of two codes [i] based on
1. 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]
2. 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		Method
1	Linear OA(4¹⁴⁶, 167, F₄, 85) (dual of [167, 21, 86]-code)	[i]	Truncation
2	Linear OA(4¹⁴⁵, 166, F₄, 84) (dual of [166, 21, 85]-code)	[i]	Truncation
3	Linear OOA(4¹⁴⁷, 84, F₄, 2, 86) (dual of [(84, 2), 21, 87]-NRT-code)	[i]	OOA Folding
4	Linear OOA(4¹⁴⁷, 56, F₄, 3, 86) (dual of [(56, 3), 21, 87]-NRT-code)	[i]	OOA Folding