MinT - Information on Result #2222085

Information on Result #2222085

Linear OA(2¹¹², 164, F₂, 36) (dual of [164, 52, 37]-code), using 1 times truncation based on linear OA(2¹¹³, 165, F₂, 37) (dual of [165, 52, 38]-code), using

concatenation of two codes [i] based on
1. linear OA(16²⁰, 33, F₁₆, 18) (dual of [33, 13, 19]-code), using
  - extended algebraic-geometric code AG_e(F,14P) [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, using
    - a function field by SÃ©mirat [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.

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		Method
1	Linear OA(2¹¹⁴, 166, F₂, 36) (dual of [166, 52, 37]-code)	[i]	Code Embedding in Larger Space
2	Linear OA(2¹¹⁵, 167, F₂, 36) (dual of [167, 52, 37]-code)	[i]
3	Linear OA(2¹¹⁶, 168, F₂, 36) (dual of [168, 52, 37]-code)	[i]
4	Linear OA(2¹¹⁷, 169, F₂, 36) (dual of [169, 52, 37]-code)	[i]
5	Linear OA(2¹¹⁶, 169, F₂, 36) (dual of [169, 53, 37]-code)	[i]	ConstructionÂ X with VarÅ¡amov Bound
6	Linear OOA(2¹¹², 82, F₂, 2, 36) (dual of [(82, 2), 52, 37]-NRT-code)	[i]	OOA Folding
7	Linear OOA(2¹¹², 54, F₂, 3, 36) (dual of [(54, 3), 50, 37]-NRT-code)	[i]	OOA Folding