MinT - Information on Result #2612664

Information on Result #2612664

Linear OOA(2¹³⁸, 92, F₂, 3, 40) (dual of [(92, 3), 138, 41]-NRT-code), using strength reduction based on linear OOA(2¹³⁸, 92, F₂, 3, 41) (dual of [(92, 3), 138, 42]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(8²³, 23, F₈, 3, 20) (dual of [(23, 3), 46, 21]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(8²³, 24, F₈, 3, 20) (dual of [(24, 3), 49, 21]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,51P) [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(2¹³⁹, 92, F₂, 3, 40) (dual of [(92, 3), 137, 41]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(2¹³⁸, 46, F₂, 6, 40) (dual of [(46, 6), 138, 41]-NRT-code)	[i]		OOA Folding