MinT - Information on Result #637084

Information on Result #637084

Linear OA(4²³³, 305, F₄, 113) (dual of [305, 72, 114]-code), using concatenation of two codes based on

linear OA(64³⁷, 61, F₆₄, 37) (dual of [61, 24, 38]-code or 61-arc in PG(36,64)), using
- discarding factors / shortening the dual code based on linear OA(64³⁷, 64, F₆₄, 37) (dual of [64, 27, 38]-code or 64-arc in PG(36,64)), using
  - Reedâ€“Solomon code RS(27,64) [i]
linear OA(4², 5, F₄, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,4)), using
- extended Reedâ€“Solomon code RS_e(3,4) [i]
- Hamming code H(2,4) [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(4²³³, 305, F₄, 112) (dual of [305, 72, 113]-code)	[i]		Strength Reduction
2	Linear OA(4²³⁴, 306, F₄, 113) (dual of [306, 72, 114]-code)	[i]		Code Embedding in Larger Space
3	Linear OA(4²³², 304, F₄, 112) (dual of [304, 72, 113]-code)	[i]		Truncation
4	Linear OA(4²³¹, 303, F₄, 111) (dual of [303, 72, 112]-code)	[i]		Truncation
5	Linear OOA(4²³³, 152, F₄, 2, 113) (dual of [(152, 2), 71, 114]-NRT-code)	[i]		OOA Folding
6	Linear OOA(4²³³, 101, F₄, 3, 113) (dual of [(101, 3), 70, 114]-NRT-code)	[i]		OOA Folding