MinT - Information on Result #2220326

Information on Result #2220326

Linear OA(2⁶⁸, 104, F₂, 22) (dual of [104, 36, 23]-code), using 1 times truncation based on linear OA(2⁶⁹, 105, F₂, 23) (dual of [105, 36, 24]-code), using

concatenation of two codes [i] based on
1. linear OA(16¹², 21, F₁₆, 11) (dual of [21, 9, 12]-code), using
  - discarding factors / shortening the dual code based on linear OA(16¹², 24, F₁₆, 11) (dual of [24, 12, 12]-code), using
    - extended algebraic-geometric code AG_e(F,12P) [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 24, using
      - a function field by SÃ©mirat [i]
2. linear OA(2¹, 5, F₂, 1) (dual of [5, 4, 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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2⁶⁸, 52, F₂, 2, 22) (dual of [(52, 2), 36, 23]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2⁶⁸, 34, F₂, 3, 22) (dual of [(34, 3), 34, 23]-NRT-code)	[i]		OOA Folding