MinT - Information on Result #637293

Information on Result #637293

Linear OA(4¹⁷⁴, 216, F₄, 91) (dual of [216, 42, 92]-code), using concatenation of two codes based on

linear OA(64²², 36, F₆₄, 22) (dual of [36, 14, 23]-code or 36-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(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(4¹⁷⁴, 216, F₄, 90) (dual of [216, 42, 91]-code)	[i]		Strength Reduction
2	Linear OA(4¹⁷⁴, 216, F₄, 89) (dual of [216, 42, 90]-code)	[i]		Strength Reduction
3	Linear OA(4¹⁷⁵, 217, F₄, 91) (dual of [217, 42, 92]-code)	[i]		Code Embedding in Larger Space
4	Linear OA(4¹⁷³, 215, F₄, 90) (dual of [215, 42, 91]-code)	[i]		Truncation
5	Linear OA(4¹⁷², 214, F₄, 89) (dual of [214, 42, 90]-code)	[i]
6	Linear OA(4¹⁷¹, 213, F₄, 88) (dual of [213, 42, 89]-code)	[i]
7	Linear OA(4¹⁷⁰, 212, F₄, 87) (dual of [212, 42, 88]-code)	[i]
8	Linear OA(4¹⁶⁹, 211, F₄, 86) (dual of [211, 42, 87]-code)	[i]
9	Linear OA(4¹⁶⁷, 209, F₄, 84) (dual of [209, 42, 85]-code)	[i]
10	Linear OA(4¹⁷⁶, 219, F₄, 91) (dual of [219, 43, 92]-code)	[i]		ConstructionÂ X with VarÅ¡amov Bound
11	Linear OOA(4¹⁷⁴, 108, F₄, 2, 91) (dual of [(108, 2), 42, 92]-NRT-code)	[i]		OOA Folding
12	Linear OOA(4¹⁷⁴, 72, F₄, 3, 91) (dual of [(72, 3), 42, 92]-NRT-code)	[i]		OOA Folding