MinT - Information on Result #2457873

Information on Result #2457873

Linear OOA(2¹²³, 74, F₂, 2, 54) (dual of [(74, 2), 25, 55]-NRT-code), using 1 step truncation based on linear OOA(2¹²⁴, 75, F₂, 2, 55) (dual of [(75, 2), 26, 56]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(4³⁷, 25, F₄, 2, 27) (dual of [(25, 2), 13, 28]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(4³⁷, 26, F₄, 2, 27) (dual of [(26, 2), 15, 28]-NRT-code), using
    - algebraic-geometric NRT-code AG(2;F,24P) [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
      - an explicitly constructive algebraic function field [i]
2. linear OA(2¹, 3, F₂, 1) (dual of [3, 2, 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(2¹²³, 37, F₂, 4, 54) (dual of [(37, 4), 25, 55]-NRT-code)	[i]		OOA Folding