MinT - Information on Result #2225986

Information on Result #2225986

Linear OA(2¹⁹², 324, F₂, 52) (dual of [324, 132, 53]-code), using 1 times truncation based on linear OA(2¹⁹³, 325, F₂, 53) (dual of [325, 132, 54]-code), using

concatenation of two codes [i] based on
1. linear OA(16³², 65, F₁₆, 26) (dual of [65, 33, 27]-code), using
  - extended algebraic-geometric code AG_e(F,38P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]
2. 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		Method
1	Linear OA(2¹⁹⁴, 326, F₂, 52) (dual of [326, 132, 53]-code)	[i]	Code Embedding in Larger Space
2	Linear OA(2¹⁹⁵, 327, F₂, 52) (dual of [327, 132, 53]-code)	[i]
3	Linear OA(2¹⁹⁶, 328, F₂, 52) (dual of [328, 132, 53]-code)	[i]
4	Linear OA(2¹⁹⁷, 329, F₂, 52) (dual of [329, 132, 53]-code)	[i]
5	Linear OA(2¹⁹⁶, 329, F₂, 52) (dual of [329, 133, 53]-code)	[i]	ConstructionÂ X with VarÅ¡amov Bound
6	Linear OOA(2¹⁹², 162, F₂, 2, 52) (dual of [(162, 2), 132, 53]-NRT-code)	[i]	OOA Folding
7	Linear OOA(2¹⁹², 108, F₂, 3, 52) (dual of [(108, 3), 132, 53]-NRT-code)	[i]	OOA Folding