MinT - Information on Result #636752

Information on Result #636752

Linear OA(4¹³¹, 170, F₄, 65) (dual of [170, 39, 66]-code), using concatenation of two codes based on

linear OA(64²¹, 34, F₆₄, 21) (dual of [34, 13, 22]-code or 34-arc in PG(20,64)), using
- discarding factors / shortening the dual code based on linear OA(64²¹, 64, F₆₄, 21) (dual of [64, 43, 22]-code or 64-arc in PG(20,64)), using
  - Reedâ€“Solomon code RS(43,64) [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.

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(4¹³¹, 170, F₄, 64) (dual of [170, 39, 65]-code)	[i]		Strength Reduction
2	Linear OA(4¹³², 171, F₄, 65) (dual of [171, 39, 66]-code)	[i]		Code Embedding in Larger Space
3	Linear OA(4¹³⁰, 169, F₄, 64) (dual of [169, 39, 65]-code)	[i]		Truncation
4	Linear OA(4¹²⁹, 168, F₄, 63) (dual of [168, 39, 64]-code)	[i]		Truncation
5	Linear OOA(4¹³¹, 85, F₄, 2, 65) (dual of [(85, 2), 39, 66]-NRT-code)	[i]		OOA Folding
6	Linear OOA(4¹³¹, 56, F₄, 3, 65) (dual of [(56, 3), 37, 66]-NRT-code)	[i]		OOA Folding