MinT - Information on Result #2225803

Information on Result #2225803

Linear OA(2¹⁸⁹, 289, F₂, 54) (dual of [289, 100, 55]-code), using 1 times truncation based on linear OA(2¹⁹⁰, 290, F₂, 55) (dual of [290, 100, 56]-code), using

concatenation of two codes [i] based on
1. linear OA(16³³, 58, F₁₆, 27) (dual of [58, 25, 28]-code), using
  - discarding factors / shortening the dual code based on linear OA(16³³, 64, F₁₆, 27) (dual of [64, 31, 28]-code), using
    - algebraic-geometric code AG(F,36P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [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(2¹⁸⁹, 144, F₂, 2, 54) (dual of [(144, 2), 99, 55]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2¹⁸⁹, 96, F₂, 3, 54) (dual of [(96, 3), 99, 55]-NRT-code)	[i]		OOA Folding