MinT - Information on Result #2224839

Information on Result #2224839

Linear OA(2²⁰³, 223, F₂, 86) (dual of [223, 20, 87]-code), using 1 times truncation based on linear OA(2²⁰⁴, 224, F₂, 87) (dual of [224, 20, 88]-code), using

concatenation of two codes [i] based on
1. linear OA(16²³, 28, F₁₆, 21) (dual of [28, 5, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(16²³, 33, F₁₆, 21) (dual of [33, 10, 22]-code), using
    - extended algebraic-geometric code AG_e(F,11P) [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.

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(2²⁰⁵, 225, F₂, 86) (dual of [225, 20, 87]-code)	[i]	Code Embedding in Larger Space
2	Linear OA(2²⁰⁶, 226, F₂, 86) (dual of [226, 20, 87]-code)	[i]	Code Embedding in Larger Space
3	Linear OOA(2²⁰³, 111, F₂, 2, 86) (dual of [(111, 2), 19, 87]-NRT-code)	[i]	OOA Folding
4	Linear OOA(2²⁰³, 74, F₂, 3, 86) (dual of [(74, 3), 19, 87]-NRT-code)	[i]	OOA Folding