MinT - Information on Result #2224594

Information on Result #2224594

Linear OA(2¹⁶⁶, 214, F₂, 54) (dual of [214, 48, 55]-code), using 1 times truncation based on linear OA(2¹⁶⁷, 215, F₂, 55) (dual of [215, 48, 56]-code), using

concatenation of two codes [i] based on
1. linear OA(16³¹, 43, F₁₆, 27) (dual of [43, 12, 28]-code), using
  - discarding factors / shortening the dual code based on linear OA(16³¹, 45, F₁₆, 27) (dual of [45, 14, 28]-code), using
    - extended algebraic-geometric code AG_e(F,17P) [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
      - a function field by GarcÃa and Quoos [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(2¹⁶⁶, 107, F₂, 2, 54) (dual of [(107, 2), 48, 55]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2¹⁶⁶, 71, F₂, 3, 54) (dual of [(71, 3), 47, 55]-NRT-code)	[i]		OOA Folding