MinT - Information on Result #2612042

Information on Result #2612042

Linear OOA(2¹²³, 57, F₂, 3, 52) (dual of [(57, 3), 48, 53]-NRT-code), using strength reduction based on linear OOA(2¹²³, 57, F₂, 3, 53) (dual of [(57, 3), 48, 54]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(4³³, 19, F₄, 3, 26) (dual of [(19, 3), 24, 27]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(4³³, 21, F₄, 3, 26) (dual of [(21, 3), 30, 27]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,36P) [i] based on function field F/F₄ with g(F) = 7 and N(F) ≥ 21, 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(2¹²⁴, 57, F₂, 3, 52) (dual of [(57, 3), 47, 53]-NRT-code)	[i]		OOA Duplication