MinT - Information on Result #2225884

Information on Result #2225884

Linear OA(2²⁰⁶, 262, F₂, 69) (dual of [262, 56, 70]-code), using 2 times truncation based on linear OA(2²⁰⁸, 264, F₂, 71) (dual of [264, 56, 72]-code), using

concatenation of two codes [i] based on
1. linear OA(16¹⁹, 33, F₁₆, 17) (dual of [33, 14, 18]-code), using
  - extended algebraic-geometric code AG_e(F,15P) [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(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(2²⁰⁹, 265, F₂, 69) (dual of [265, 56, 70]-code)	[i]		Code Embedding in Larger Space
2	Linear OA(2²¹⁰, 266, F₂, 69) (dual of [266, 56, 70]-code)	[i]
3	Linear OA(2²¹¹, 267, F₂, 69) (dual of [267, 56, 70]-code)	[i]
4	Linear OA(2²¹², 268, F₂, 69) (dual of [268, 56, 70]-code)	[i]
5	Linear OA(2²¹³, 269, F₂, 69) (dual of [269, 56, 70]-code)	[i]
6	Linear OA(2²¹³, 272, F₂, 68) (dual of [272, 59, 69]-code)	[i]		ConstructionÂ X with VarÅ¡amov Bound
7	Linear OOA(2²⁰⁶, 131, F₂, 2, 69) (dual of [(131, 2), 56, 70]-NRT-code)	[i]		OOA Folding
8	Linear OOA(2²⁰⁶, 87, F₂, 3, 69) (dual of [(87, 3), 55, 70]-NRT-code)	[i]		OOA Folding