MinT - Information on Result #2422740

Information on Result #2422740

Linear OOA(2¹⁸⁰, 170, F₂, 2, 50) (dual of [(170, 2), 160, 51]-NRT-code), using strength reduction based on linear OOA(2¹⁸⁰, 170, F₂, 2, 51) (dual of [(170, 2), 160, 52]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(16²⁸, 34, F₁₆, 2, 25) (dual of [(34, 2), 40, 26]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(16²⁸, 38, F₁₆, 2, 25) (dual of [(38, 2), 48, 26]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,50P) [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, 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, 85, F₂, 4, 50) (dual of [(85, 4), 160, 51]-NRT-code)	[i]		OOA Folding