MinT - Information on Result #2225044

Information on Result #2225044

Linear OA(2¹⁹⁹, 231, F₂, 78) (dual of [231, 32, 79]-code), using 1 times truncation based on linear OA(2²⁰⁰, 232, F₂, 79) (dual of [232, 32, 80]-code), using

concatenation of two codes [i] based on
1. linear OA(16²¹, 29, F₁₆, 19) (dual of [29, 8, 20]-code), using
  - discarding factors / shortening the dual code based on linear OA(16²¹, 33, F₁₆, 19) (dual of [33, 12, 20]-code), using
    - extended algebraic-geometric code AG_e(F,13P) [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(2²⁰¹, 233, F₂, 78) (dual of [233, 32, 79]-code)	[i]	Code Embedding in Larger Space
2	Linear OOA(2¹⁹⁹, 115, F₂, 2, 78) (dual of [(115, 2), 31, 79]-NRT-code)	[i]	OOA Folding
3	Linear OOA(2¹⁹⁹, 77, F₂, 3, 78) (dual of [(77, 3), 32, 79]-NRT-code)	[i]	OOA Folding