MinT - Information on Result #636861

Information on Result #636861

Linear OA(4²⁰⁹, 305, F₄, 89) (dual of [305, 96, 90]-code), using concatenation of two codes based on

linear OA(64²⁹, 61, F₆₄, 29) (dual of [61, 32, 30]-code or 61-arc in PG(28,64)), using
- discarding factors / shortening the dual code based on linear OA(64²⁹, 64, F₆₄, 29) (dual of [64, 35, 30]-code or 64-arc in PG(28,64)), using
  - Reedâ€“Solomon code RS(35,64) [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(4²⁰⁹, 305, F₄, 88) (dual of [305, 96, 89]-code)	[i]		Strength Reduction
2	Linear OA(4²¹⁰, 306, F₄, 89) (dual of [306, 96, 90]-code)	[i]		Code Embedding in Larger Space
3	Linear OA(4²⁰⁸, 304, F₄, 88) (dual of [304, 96, 89]-code)	[i]		Truncation
4	Linear OA(4²⁰⁷, 303, F₄, 87) (dual of [303, 96, 88]-code)	[i]		Truncation
5	Linear OOA(4²⁰⁹, 152, F₄, 2, 89) (dual of [(152, 2), 95, 90]-NRT-code)	[i]		OOA Folding
6	Linear OOA(4²⁰⁹, 101, F₄, 3, 89) (dual of [(101, 3), 94, 90]-NRT-code)	[i]		OOA Folding