MinT - Information on Result #2202421

Information on Result #2202421

Linear OA(4¹⁴⁴, 174, F₄, 78) (dual of [174, 30, 79]-code), using strength reduction based on linear OA(4¹⁴⁴, 174, F₄, 79) (dual of [174, 30, 80]-code), using

concatenation of two codes [i] based on
1. linear OA(64¹⁹, 29, F₆₄, 19) (dual of [29, 10, 20]-code or 29-arc in PG(18,64)), using
  - discarding factors / shortening the dual code based on linear OA(64¹⁹, 64, F₆₄, 19) (dual of [64, 45, 20]-code or 64-arc in PG(18,64)), using
    - Reedâ€“Solomon code RS(45,64) [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(4¹⁴³, 173, F₄, 77) (dual of [173, 30, 78]-code)	[i]	Truncation
2	Linear OA(4¹⁴², 172, F₄, 76) (dual of [172, 30, 77]-code)	[i]	Truncation
3	Linear OOA(4¹⁴⁴, 87, F₄, 2, 78) (dual of [(87, 2), 30, 79]-NRT-code)	[i]	OOA Folding
4	Linear OOA(4¹⁴⁴, 58, F₄, 3, 78) (dual of [(58, 3), 30, 79]-NRT-code)	[i]	OOA Folding