MinT - Information on Result #2458013

Information on Result #2458013

Linear OOA(2¹⁰⁹, 87, F₂, 2, 38) (dual of [(87, 2), 65, 39]-NRT-code), using 1 step truncation based on linear OOA(2¹¹⁰, 88, F₂, 2, 39) (dual of [(88, 2), 66, 40]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(8²², 22, F₈, 2, 19) (dual of [(22, 2), 22, 20]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(8²², 24, F₈, 2, 19) (dual of [(24, 2), 26, 20]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,28P) [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, 43, F₂, 4, 38) (dual of [(43, 4), 63, 39]-NRT-code)	[i]		OOA Folding