MinT - Information on Result #637368

Information on Result #637368

Linear OA(4²⁰⁷, 246, F₄, 115) (dual of [246, 39, 116]-code), using concatenation of two codes based on

linear OA(64²⁸, 41, F₆₄, 28) (dual of [41, 13, 29]-code or 41-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.

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(4²⁰⁷, 246, F₄, 114) (dual of [246, 39, 115]-code)	[i]		Strength Reduction
2	Linear OA(4²⁰⁷, 246, F₄, 113) (dual of [246, 39, 114]-code)	[i]		Strength Reduction
3	Linear OA(4²⁰⁸, 247, F₄, 115) (dual of [247, 39, 116]-code)	[i]		Code Embedding in Larger Space
4	Linear OA(4²⁰⁶, 245, F₄, 114) (dual of [245, 39, 115]-code)	[i]		Truncation
5	Linear OA(4²⁰⁵, 244, F₄, 113) (dual of [244, 39, 114]-code)	[i]
6	Linear OA(4²⁰⁴, 243, F₄, 112) (dual of [243, 39, 113]-code)	[i]
7	Linear OA(4²⁰³, 242, F₄, 111) (dual of [242, 39, 112]-code)	[i]
8	Linear OA(4²⁰², 241, F₄, 110) (dual of [241, 39, 111]-code)	[i]
9	Linear OA(4²⁰⁰, 239, F₄, 108) (dual of [239, 39, 109]-code)	[i]
10	Linear OOA(4²⁰⁷, 123, F₄, 2, 115) (dual of [(123, 2), 39, 116]-NRT-code)	[i]		OOA Folding
11	Linear OOA(4²⁰⁷, 82, F₄, 3, 115) (dual of [(82, 3), 39, 116]-NRT-code)	[i]		OOA Folding