MinT - Information on Result #636972

Information on Result #636972

Linear OA(4²⁰⁹, 275, F₄, 101) (dual of [275, 66, 102]-code), using concatenation of two codes based on

linear OA(64³³, 55, F₆₄, 33) (dual of [55, 22, 34]-code or 55-arc in PG(32,64)), using
- discarding factors / shortening the dual code based on linear OA(64³³, 64, F₆₄, 33) (dual of [64, 31, 34]-code or 64-arc in PG(32,64)), using
  - Reedâ€“Solomon code RS(31,64) [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, 275, F₄, 100) (dual of [275, 66, 101]-code)	[i]		Strength Reduction
2	Linear OA(4²¹⁰, 276, F₄, 101) (dual of [276, 66, 102]-code)	[i]		Code Embedding in Larger Space
3	Linear OA(4²⁰⁸, 274, F₄, 100) (dual of [274, 66, 101]-code)	[i]		Truncation
4	Linear OA(4²⁰⁷, 273, F₄, 99) (dual of [273, 66, 100]-code)	[i]		Truncation
5	Linear OOA(4²⁰⁹, 137, F₄, 2, 101) (dual of [(137, 2), 65, 102]-NRT-code)	[i]		OOA Folding
6	Linear OOA(4²⁰⁹, 91, F₄, 3, 101) (dual of [(91, 3), 64, 102]-NRT-code)	[i]		OOA Folding