MinT - Information on Result #629829

Information on Result #629829

Linear OA(2¹⁸¹, 325, F₂, 47) (dual of [325, 144, 48]-code), using concatenation of two codes based on

linear OA(16²⁹, 65, F₁₆, 23) (dual of [65, 36, 24]-code), using
- extended algebraic-geometric code AG_e(F,41P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
  - the Hermitian function field over F₁₆ [i]
linear OA(2¹, 5, F₂, 1) (dual of [5, 4, 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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OA(2¹⁸¹, 325, F₂, 46) (dual of [325, 144, 47]-code)	[i]		Strength Reduction
2	Linear OA(2¹⁸², 326, F₂, 47) (dual of [326, 144, 48]-code)	[i]		Code Embedding in Larger Space
3	Linear OA(2¹⁸³, 327, F₂, 47) (dual of [327, 144, 48]-code)	[i]
4	Linear OA(2¹⁸⁴, 328, F₂, 47) (dual of [328, 144, 48]-code)	[i]
5	Linear OA(2¹⁸⁰, 324, F₂, 46) (dual of [324, 144, 47]-code)	[i]		Truncation
6	Linear OOA(2¹⁸¹, 162, F₂, 2, 47) (dual of [(162, 2), 143, 48]-NRT-code)	[i]		OOA Folding
7	Linear OOA(2¹⁸¹, 108, F₂, 3, 47) (dual of [(108, 3), 143, 48]-NRT-code)	[i]		OOA Folding