MinT - Information on Result #636724

Information on Result #636724

Linear OA(4¹²³, 165, F₄, 59) (dual of [165, 42, 60]-code), using concatenation of two codes based on

linear OA(64¹⁹, 33, F₆₄, 19) (dual of [33, 14, 20]-code or 33-arc in PG(18,64)), using
- discarding factors / shortening the dual code based on linear OA(64¹⁹, 64, F₆₄, 19) (dual of [64, 45, 20]-code or 64-arc in PG(18,64)), using
  - Reedâ€“Solomon code RS(45,64) [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(4¹²³, 165, F₄, 58) (dual of [165, 42, 59]-code)	[i]		Strength Reduction
2	Linear OA(4¹²⁴, 166, F₄, 59) (dual of [166, 42, 60]-code)	[i]		Code Embedding in Larger Space
3	Linear OA(4¹²², 164, F₄, 58) (dual of [164, 42, 59]-code)	[i]		Truncation
4	Linear OA(4¹²¹, 163, F₄, 57) (dual of [163, 42, 58]-code)	[i]		Truncation
5	Linear OOA(4¹²³, 82, F₄, 2, 59) (dual of [(82, 2), 41, 60]-NRT-code)	[i]		OOA Folding
6	Linear OOA(4¹²³, 55, F₄, 3, 59) (dual of [(55, 3), 42, 60]-NRT-code)	[i]		OOA Folding