MinT - Information on Result #2223062

Information on Result #2223062

Linear OA(2¹³⁹, 175, F₂, 50) (dual of [175, 36, 51]-code), using 1 times truncation based on linear OA(2¹⁴⁰, 176, F₂, 51) (dual of [176, 36, 52]-code), using

concatenation of two codes [i] based on
1. linear OA(16¹³, 22, F₁₆, 12) (dual of [22, 9, 13]-code), using
  - discarding factors / shortening the dual code based on linear OA(16¹³, 24, F₁₆, 12) (dual of [24, 11, 13]-code), using
    - extended algebraic-geometric code AG_e(F,11P) [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 24, 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		This result only	Method
1	Linear OOA(2¹³⁹, 87, F₂, 2, 50) (dual of [(87, 2), 35, 51]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2¹³⁹, 58, F₂, 3, 50) (dual of [(58, 3), 35, 51]-NRT-code)	[i]		OOA Folding