MinT - Information on Result #2611505

Information on Result #2611505

Linear OOA(2¹⁰⁹, 45, F₂, 3, 56) (dual of [(45, 3), 26, 57]-NRT-code), using strength reduction based on linear OOA(2¹⁰⁹, 45, F₂, 3, 57) (dual of [(45, 3), 26, 58]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(4³², 15, F₄, 3, 28) (dual of [(15, 3), 13, 29]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,16P) [i] based on function field F/F₄ with g(F) = 4 and N(F) ≥ 15, using
    - an explicitly constructive algebraic function field [i]
2. linear OA(2¹, 3, F₂, 1) (dual of [3, 2, 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(2¹¹², 46, F₂, 3, 56) (dual of [(46, 3), 26, 57]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
2	Linear OOA(2¹¹⁰, 45, F₂, 3, 56) (dual of [(45, 3), 25, 57]-NRT-code)	[i]		OOA Duplication