MinT - Information on Result #2609961

Information on Result #2609961

Linear OOA(2⁵⁰, 24, F₂, 3, 24) (dual of [(24, 3), 22, 25]-NRT-code), using strength reduction based on linear OOA(2⁵⁰, 24, F₂, 3, 25) (dual of [(24, 3), 22, 26]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(4¹³, 8, F₄, 3, 12) (dual of [(8, 3), 11, 13]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(4¹³, 9, F₄, 3, 12) (dual of [(9, 3), 14, 13]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,14P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
      - the Hermitian function field over F₄ [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		Method
1	Linear OOA(2⁵¹, 24, F₂, 3, 24) (dual of [(24, 3), 21, 25]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2⁵⁰, 12, F₂, 5, 24) (dual of [(12, 5), 10, 25]-NRT-code)	[i]	OOA Folding
3	Linear OOA(2⁵⁰, 12, F₂, 6, 24) (dual of [(12, 6), 22, 25]-NRT-code)	[i]	OOA Folding