MinT - Information on Result #637244

Information on Result #637244

Linear OA(4¹²⁹, 162, F₄, 67) (dual of [162, 33, 68]-code), using concatenation of two codes based on

linear OA(64¹⁶, 27, F₆₄, 16) (dual of [27, 11, 17]-code or 27-arc in PG(15,64)), using
- discarding factors / shortening the dual code based on linear OA(64¹⁶, 64, F₆₄, 16) (dual of [64, 48, 17]-code or 64-arc in PG(15,64)), using
  - Reedâ€“Solomon code RS(48,64) [i]
linear OA(4³, 6, F₄, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,4) or 6-cap in PG(2,4)), using
- hyperoval in PG(2,Â 4) [i]
- the Hexacode [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(4¹²⁹, 162, F₄, 66) (dual of [162, 33, 67]-code)	[i]		Strength Reduction
2	Linear OA(4¹³⁰, 163, F₄, 67) (dual of [163, 33, 68]-code)	[i]		Code Embedding in Larger Space
3	Linear OA(4¹²⁸, 161, F₄, 66) (dual of [161, 33, 67]-code)	[i]		Truncation
4	Linear OA(4¹²⁶, 159, F₄, 64) (dual of [159, 33, 65]-code)	[i]
5	Linear OA(4¹²⁵, 158, F₄, 63) (dual of [158, 33, 64]-code)	[i]
6	Linear OOA(4¹²⁹, 81, F₄, 2, 67) (dual of [(81, 2), 33, 68]-NRT-code)	[i]		OOA Folding
7	Linear OOA(4¹²⁹, 54, F₄, 3, 67) (dual of [(54, 3), 33, 68]-NRT-code)	[i]		OOA Folding