MinT - Information on Result #738050

Information on Result #738050

Linear OA(2⁴², 54, F₂, 19) (dual of [54, 12, 20]-code), using concatenation of two codes based on

linear OA(4¹², 18, F₄, 9) (dual of [18, 6, 10]-code), using
- a quaternary quasi-twisted code of dimension 6 by Gulliver and Ã–stergÃ¥rd [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(2⁴², 54, F₂, 18) (dual of [54, 12, 19]-code)	[i]		Strength Reduction
2	Linear OA(2⁴³, 55, F₂, 19) (dual of [55, 12, 20]-code)	[i]		Code Embedding in Larger Space
3	Linear OA(2⁴¹, 53, F₂, 18) (dual of [53, 12, 19]-code)	[i]		Truncation
4	Linear OOA(2⁴², 27, F₂, 2, 19) (dual of [(27, 2), 12, 20]-NRT-code)	[i]		OOA Folding
5	Linear OOA(2⁴², 18, F₂, 3, 19) (dual of [(18, 3), 12, 20]-NRT-code)	[i]		OOA Folding