MinT - Information on Result #2459304

Information on Result #2459304

Linear OOA(2¹⁴⁹, 107, F₂, 2, 54) (dual of [(107, 2), 65, 55]-NRT-code), using 1 step truncation based on linear OOA(2¹⁵⁰, 108, F₂, 2, 55) (dual of [(108, 2), 66, 56]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(8³², 27, F₈, 2, 27) (dual of [(27, 2), 22, 28]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(8³², 28, F₈, 2, 27) (dual of [(28, 2), 24, 28]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,28P) [i] based on function field F/F₈ with g(F) = 5 and N(F) ≥ 28, using
      - a function field by SÃ©mirat [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(2¹⁴⁹, 53, F₂, 4, 54) (dual of [(53, 4), 63, 55]-NRT-code)	[i]		OOA Folding