MinT - Information on Result #636751

Information on Result #636751

Linear OA(4¹³³, 175, F₄, 65) (dual of [175, 42, 66]-code), using concatenation of two codes based on

linear OA(64²¹, 35, F₆₄, 21) (dual of [35, 14, 22]-code or 35-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(4¹³³, 175, F₄, 64) (dual of [175, 42, 65]-code)	[i]		Strength Reduction
2	Linear OA(4¹³⁴, 176, F₄, 65) (dual of [176, 42, 66]-code)	[i]		Code Embedding in Larger Space
3	Linear OA(4¹³², 174, F₄, 64) (dual of [174, 42, 65]-code)	[i]		Truncation
4	Linear OA(4¹³¹, 173, F₄, 63) (dual of [173, 42, 64]-code)	[i]		Truncation
5	Linear OOA(4¹³³, 87, F₄, 2, 65) (dual of [(87, 2), 41, 66]-NRT-code)	[i]		OOA Folding
6	Linear OOA(4¹³³, 58, F₄, 3, 65) (dual of [(58, 3), 41, 66]-NRT-code)	[i]		OOA Folding