MinT - Information on Result #637362

Information on Result #637362

Linear OA(4²²⁵, 282, F₄, 115) (dual of [282, 57, 116]-code), using concatenation of two codes based on

linear OA(64²⁸, 47, F₆₄, 28) (dual of [47, 19, 29]-code or 47-arc in PG(27,64)), using
- discarding factors / shortening the dual code based on linear OA(64²⁸, 64, F₆₄, 28) (dual of [64, 36, 29]-code or 64-arc in PG(27,64)), using
  - Reedâ€“Solomon code RS(36,64) [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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OA(4²²⁵, 282, F₄, 114) (dual of [282, 57, 115]-code)	[i]		Strength Reduction
2	Linear OA(4²²⁶, 283, F₄, 115) (dual of [283, 57, 116]-code)	[i]		Code Embedding in Larger Space
3	Linear OA(4²²⁴, 281, F₄, 114) (dual of [281, 57, 115]-code)	[i]		Truncation
4	Linear OA(4²²², 279, F₄, 112) (dual of [279, 57, 113]-code)	[i]
5	Linear OA(4²²¹, 278, F₄, 111) (dual of [278, 57, 112]-code)	[i]
6	Linear OOA(4²²⁵, 141, F₄, 2, 115) (dual of [(141, 2), 57, 116]-NRT-code)	[i]		OOA Folding
7	Linear OOA(4²²⁵, 94, F₄, 3, 115) (dual of [(94, 3), 57, 116]-NRT-code)	[i]		OOA Folding