MinT - Information on Result #2457749

Information on Result #2457749

Linear OOA(2¹⁰⁹, 75, F₂, 2, 42) (dual of [(75, 2), 41, 43]-NRT-code), using 1 step truncation based on linear OOA(2¹¹⁰, 76, F₂, 2, 43) (dual of [(76, 2), 42, 44]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(8²⁴, 19, F₈, 2, 21) (dual of [(19, 2), 14, 22]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(8²⁴, 24, F₈, 2, 21) (dual of [(24, 2), 24, 22]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,26P) [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
      - the Klein quartic over F₈ [i]
2. linear OA(2¹, 4, F₂, 1) (dual of [4, 3, 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(2¹⁰⁹, 37, F₂, 4, 42) (dual of [(37, 4), 39, 43]-NRT-code)	[i]		OOA Folding