MinT - Information on Result #2422739

Information on Result #2422739

Linear OOA(2¹⁸⁰, 160, F₂, 2, 54) (dual of [(160, 2), 140, 55]-NRT-code), using strength reduction based on linear OOA(2¹⁸⁰, 160, F₂, 2, 55) (dual of [(160, 2), 140, 56]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(16²⁹, 32, F₁₆, 2, 27) (dual of [(32, 2), 35, 28]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(16²⁹, 33, F₁₆, 2, 27) (dual of [(33, 2), 37, 28]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,38P) [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(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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2¹⁸⁰, 80, F₂, 4, 54) (dual of [(80, 4), 140, 55]-NRT-code)	[i]		OOA Folding