MinT - Information on Result #629485

Information on Result #629485

Linear OA(2⁶⁹, 96, F₂, 25) (dual of [96, 27, 26]-code), using concatenation of two codes based on

linear OA(8¹⁵, 24, F₈, 12) (dual of [24, 9, 13]-code), using
- extended algebraic-geometric code AG_e(F,11P) [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
  - the Klein quartic over F₈ [i]
linear OA(2¹, 4, F₂, 1) (dual of [4, 3, 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(2⁶⁹, 96, F₂, 24) (dual of [96, 27, 25]-code)	[i]		Strength Reduction
2	Linear OA(2⁷⁰, 97, F₂, 25) (dual of [97, 27, 26]-code)	[i]		Code Embedding in Larger Space
3	Linear OA(2⁶⁸, 95, F₂, 24) (dual of [95, 27, 25]-code)	[i]		Truncation
4	Linear OOA(2⁶⁹, 48, F₂, 2, 25) (dual of [(48, 2), 27, 26]-NRT-code)	[i]		OOA Folding
5	Linear OOA(2⁶⁹, 32, F₂, 3, 25) (dual of [(32, 3), 27, 26]-NRT-code)	[i]		OOA Folding