MinT - Information on Result #2219462

Information on Result #2219462

Linear OA(2³⁶, 44, F₂, 18) (dual of [44, 8, 19]-code), using 1 times truncation based on linear OA(2³⁷, 45, F₂, 19) (dual of [45, 8, 20]-code), using

concatenation of two codes [i] based on
1. linear OA(4¹¹, 15, F₄, 9) (dual of [15, 4, 10]-code), using
  - 2 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]
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(2¹⁶⁴, 172, F₂, 82) (dual of [172, 8, 83]-code)	[i]		Juxtaposition
2	Linear OOA(2³⁶, 22, F₂, 2, 18) (dual of [(22, 2), 8, 19]-NRT-code)	[i]		OOA Folding
3	Linear OOA(2³⁶, 14, F₂, 3, 18) (dual of [(14, 3), 6, 19]-NRT-code)	[i]		OOA Folding