MinT - Information on Result #637024

Information on Result #637024

Linear OA(4²³¹, 315, F₄, 107) (dual of [315, 84, 108]-code), using concatenation of two codes based on

linear OA(64³⁵, 63, F₆₄, 35) (dual of [63, 28, 36]-code or 63-arc in PG(34,64)), using
- discarding factors / shortening the dual code based on linear OA(64³⁵, 64, F₆₄, 35) (dual of [64, 29, 36]-code or 64-arc in PG(34,64)), using
  - Reedâ€“Solomon code RS(29,64) [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(4²³¹, 315, F₄, 106) (dual of [315, 84, 107]-code)	[i]		Strength Reduction
2	Linear OA(4²³², 316, F₄, 107) (dual of [316, 84, 108]-code)	[i]		Code Embedding in Larger Space
3	Linear OA(4²³⁰, 314, F₄, 106) (dual of [314, 84, 107]-code)	[i]		Truncation
4	Linear OA(4²²⁹, 313, F₄, 105) (dual of [313, 84, 106]-code)	[i]		Truncation
5	Linear OOA(4²³¹, 157, F₄, 2, 107) (dual of [(157, 2), 83, 108]-NRT-code)	[i]		OOA Folding
6	Linear OOA(4²³¹, 105, F₄, 3, 107) (dual of [(105, 3), 84, 108]-NRT-code)	[i]		OOA Folding