MinT - Information on Result #2175945

Information on Result #2175945

Linear OA(2⁶⁰, 90, F₂, 22) (dual of [90, 30, 23]-code), using strength reduction based on linear OA(2⁶⁰, 90, F₂, 23) (dual of [90, 30, 24]-code), using

concatenation of two codes [i] based on
1. linear OA(4¹⁵, 30, F₄, 11) (dual of [30, 15, 12]-code), using
  - extended quadratic residue code Q_e(30,4) [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(2⁵⁹, 89, F₂, 21) (dual of [89, 30, 22]-code)	[i]		Truncation
2	Linear OA(2⁵⁸, 88, F₂, 20) (dual of [88, 30, 21]-code)	[i]		Truncation
3	Linear OOA(2⁶⁰, 45, F₂, 2, 22) (dual of [(45, 2), 30, 23]-NRT-code)	[i]		OOA Folding
4	Linear OOA(2⁶⁰, 30, F₂, 3, 22) (dual of [(30, 3), 30, 23]-NRT-code)	[i]		OOA Folding