MinT - Information on Result #2219371

Information on Result #2219371

Linear OA(2¹⁹, 26, F₂, 10) (dual of [26, 7, 11]-code), using 1 times truncation based on linear OA(2²⁰, 27, F₂, 11) (dual of [27, 7, 12]-code), using

residual code [i] based on linear OA(2⁴³, 51, F₂, 23) (dual of [51, 8, 24]-code), using
- concatenation of two codes [i] based on
  1. linear OA(4¹³, 17, F₄, 11) (dual of [17, 4, 12]-code), using
    - projective code from ovoid in PG(3,Â 4) [i]
  2. 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(2¹⁵⁰, 171, F₂, 62) (dual of [171, 21, 63]-code)	[i]		ConstructionÂ XX with Cyclic Codes
2	Linear OOA(2¹⁹, 13, F₂, 2, 10) (dual of [(13, 2), 7, 11]-NRT-code)	[i]		OOA Folding
3	Linear OOA(2¹⁹, 8, F₂, 3, 10) (dual of [(8, 3), 5, 11]-NRT-code)	[i]		OOA Folding