MinT - Information on Result #636712

Information on Result #636712

Linear OA(4¹²⁰, 165, F₄, 56) (dual of [165, 45, 57]-code), using concatenation of two codes based on

linear OA(64¹⁸, 33, F₆₄, 18) (dual of [33, 15, 19]-code or 33-arc in PG(17,64)), using
- discarding factors / shortening the dual code based on linear OA(64¹⁸, 64, F₆₄, 18) (dual of [64, 46, 19]-code or 64-arc in PG(17,64)), using
  - Reedâ€“Solomon code RS(46,64) [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(4¹²⁰, 165, F₄, 55) (dual of [165, 45, 56]-code)	[i]		Strength Reduction
2	Linear OA(4¹²¹, 166, F₄, 56) (dual of [166, 45, 57]-code)	[i]		Code Embedding in Larger Space
3	Linear OA(4¹¹⁹, 164, F₄, 55) (dual of [164, 45, 56]-code)	[i]		Truncation
4	Linear OA(4¹¹⁸, 163, F₄, 54) (dual of [163, 45, 55]-code)	[i]		Truncation
5	Linear OOA(4¹²⁰, 82, F₄, 2, 56) (dual of [(82, 2), 44, 57]-NRT-code)	[i]		OOA Folding
6	Linear OOA(4¹²⁰, 55, F₄, 3, 56) (dual of [(55, 3), 45, 57]-NRT-code)	[i]		OOA Folding