MinT - Information on Result #629262

Information on Result #629262

Linear OA(2³⁴, 42, F₂, 17) (dual of [42, 8, 18]-code), using concatenation of two codes based on

linear OA(4¹⁰, 14, F₄, 8) (dual of [14, 4, 9]-code), using
- 3 times truncation [i] based on linear OA(4¹³, 17, F₄, 11) (dual of [17, 4, 12]-code), using
  - projective code from ovoid in PG(3,Â 4) [i]
linear OA(2¹, 3, F₂, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
  - parity-check code [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(2³⁴, 42, F₂, 16) (dual of [42, 8, 17]-code)	[i]		Strength Reduction
2	Linear OA(2³³, 41, F₂, 16) (dual of [41, 8, 17]-code)	[i]		Truncation
3	Linear OA(2¹⁶¹, 169, F₂, 81) (dual of [169, 8, 82]-code)	[i]		ConstructionÂ X with Extended Narrow-Sense BCH Codes
4	Linear OOA(2³⁴, 21, F₂, 2, 17) (dual of [(21, 2), 8, 18]-NRT-code)	[i]		OOA Folding
5	Linear OOA(2³⁴, 14, F₂, 3, 17) (dual of [(14, 3), 8, 18]-NRT-code)	[i]		OOA Folding