MinT - Information on Result #2657598

Information on Result #2657598

Linear OOA(2²¹⁸, 127, F₂, 3, 68) (dual of [(127, 3), 163, 69]-NRT-code), using 1 step truncation based on linear OOA(2²¹⁹, 128, F₂, 3, 69) (dual of [(128, 3), 165, 70]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(8⁴¹, 32, F₈, 3, 34) (dual of [(32, 3), 55, 35]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(8⁴¹, 34, F₈, 3, 34) (dual of [(34, 3), 61, 35]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,67P) [i] based on function field F/F₈ with g(F) = 7 and N(F) ≥ 34, 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(2²¹⁸, 63, F₂, 5, 68) (dual of [(63, 5), 97, 69]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2²¹⁸, 63, F₂, 6, 68) (dual of [(63, 6), 160, 69]-NRT-code)	[i]		OOA Folding