MinT - Information on Result #2419377

Information on Result #2419377

Linear OOA(2¹²⁴, 78, F₂, 2, 52) (dual of [(78, 2), 32, 53]-NRT-code), using strength reduction based on linear OOA(2¹²⁴, 78, F₂, 2, 53) (dual of [(78, 2), 32, 54]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(4³⁶, 26, F₄, 2, 26) (dual of [(26, 2), 16, 27]-NRT-code), using
  - algebraic-geometric NRT-code AG(2;F,25P) [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(2¹²⁴, 39, F₂, 4, 52) (dual of [(39, 4), 32, 53]-NRT-code)	[i]		OOA Folding