MinT - Information on Result #2226524

Information on Result #2226524

Linear OA(2²⁴⁵, 301, F₂, 84) (dual of [301, 56, 85]-code), using 3 times truncation based on linear OA(2²⁴⁸, 304, F₂, 87) (dual of [304, 56, 88]-code), using

concatenation of two codes [i] based on
1. linear OA(16²⁴, 38, F₁₆, 21) (dual of [38, 14, 22]-code), using
  - extended algebraic-geometric code AG_e(F,16P) [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
    - a function field by SÃ©mirat [i]
2. linear OA(2⁴, 8, F₂, 3) (dual of [8, 4, 4]-code or 8-cap in PG(3,2)), using
  - Reedâ€“Muller code RM(1,3) [i]
  - caps in base bÂ =Â 2 [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(2²⁴⁹, 305, F₂, 84) (dual of [305, 56, 85]-code)	[i]		Code Embedding in Larger Space
2	Linear OA(2²⁵⁰, 306, F₂, 84) (dual of [306, 56, 85]-code)	[i]
3	Linear OA(2²⁵¹, 307, F₂, 84) (dual of [307, 56, 85]-code)	[i]
4	Linear OA(2²⁵², 308, F₂, 84) (dual of [308, 56, 85]-code)	[i]
5	Linear OA(2²⁵⁰, 307, F₂, 84) (dual of [307, 57, 85]-code)	[i]		ConstructionÂ X with VarÅ¡amov Bound
6	Linear OOA(2²⁴⁵, 150, F₂, 2, 84) (dual of [(150, 2), 55, 85]-NRT-code)	[i]		OOA Folding
7	Linear OOA(2²⁴⁵, 100, F₂, 3, 84) (dual of [(100, 3), 55, 85]-NRT-code)	[i]		OOA Folding