MinT - Information on Result #2223680

Information on Result #2223680

Linear OA(2¹³⁷, 209, F₂, 40) (dual of [209, 72, 41]-code), using 1 times truncation based on linear OA(2¹³⁸, 210, F₂, 41) (dual of [210, 72, 42]-code), using

concatenation of two codes [i] based on
1. linear OA(16²⁴, 42, F₁₆, 20) (dual of [42, 18, 21]-code), using
  - discarding factors / shortening the dual code based on linear OA(16²⁴, 45, F₁₆, 20) (dual of [45, 21, 21]-code), using
    - extended algebraic-geometric code AG_e(F,24P) [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
      - a function field by GarcÃa and Quoos [i]
2. linear OA(2¹, 5, F₂, 1) (dual of [5, 4, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [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(2¹³⁷, 104, F₂, 2, 40) (dual of [(104, 2), 71, 41]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2¹³⁷, 69, F₂, 3, 40) (dual of [(69, 3), 70, 41]-NRT-code)	[i]		OOA Folding