MinT - Information on Result #2226277

Information on Result #2226277

Linear OA(2²¹², 324, F₂, 62) (dual of [324, 112, 63]-code), using 1 times truncation based on linear OA(2²¹³, 325, F₂, 63) (dual of [325, 112, 64]-code), using

concatenation of two codes [i] based on
1. linear OA(16³⁷, 65, F₁₆, 31) (dual of [65, 28, 32]-code), using
  - extended algebraic-geometric code AG_e(F,33P) [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(2²¹⁴, 326, F₂, 62) (dual of [326, 112, 63]-code)	[i]	Code Embedding in Larger Space
2	Linear OA(2²¹⁵, 327, F₂, 62) (dual of [327, 112, 63]-code)	[i]
3	Linear OA(2²¹⁶, 328, F₂, 62) (dual of [328, 112, 63]-code)	[i]
4	Linear OA(2²¹⁷, 329, F₂, 62) (dual of [329, 112, 63]-code)	[i]
5	Linear OA(2²¹⁷, 330, F₂, 62) (dual of [330, 113, 63]-code)	[i]	ConstructionÂ X with VarÅ¡amov Bound
6	Linear OOA(2²¹², 162, F₂, 2, 62) (dual of [(162, 2), 112, 63]-NRT-code)	[i]	OOA Folding
7	Linear OOA(2²¹², 108, F₂, 3, 62) (dual of [(108, 3), 112, 63]-NRT-code)	[i]	OOA Folding