MinT - Information on Result #738055

Information on Result #738055

Linear OA(2¹¹⁹, 129, F₂, 59) (dual of [129, 10, 60]-code), using concatenation of two codes based on

linear OA(4³⁸, 43, F₄, 29) (dual of [43, 5, 30]-code), using
- an explicit generator matrix [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(2¹¹⁹, 129, F₂, 58) (dual of [129, 10, 59]-code)	[i]		Strength Reduction
2	Linear OA(2¹¹⁹, 129, F₂, 57) (dual of [129, 10, 58]-code)	[i]		Strength Reduction
3	Linear OA(2¹²⁰, 130, F₂, 59) (dual of [130, 10, 60]-code)	[i]		Code Embedding in Larger Space
4	Linear OA(2¹²¹, 131, F₂, 59) (dual of [131, 10, 60]-code)	[i]		Code Embedding in Larger Space
5	Linear OA(2¹¹⁸, 128, F₂, 58) (dual of [128, 10, 59]-code)	[i]		Truncation
6	Linear OOA(2¹¹⁹, 64, F₂, 2, 59) (dual of [(64, 2), 9, 60]-NRT-code)	[i]		OOA Folding
7	Linear OOA(2¹¹⁹, 43, F₂, 3, 59) (dual of [(43, 3), 10, 60]-NRT-code)	[i]		OOA Folding