MinT - Information on Result #2461440

Information on Result #2461440

Linear OOA(2²⁰⁷, 219, F₂, 2, 52) (dual of [(219, 2), 231, 53]-NRT-code), using 1 step truncation based on linear OOA(2²⁰⁸, 220, F₂, 2, 53) (dual of [(220, 2), 232, 54]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(16³⁰, 44, F₁₆, 2, 26) (dual of [(44, 2), 58, 27]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(16³⁰, 45, F₁₆, 2, 26) (dual of [(45, 2), 60, 27]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,63P) [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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2²⁰⁷, 109, F₂, 4, 52) (dual of [(109, 4), 229, 53]-NRT-code)	[i]		OOA Folding