MinT - Information on Result #2230983

Information on Result #2230983

Linear OA(3¹²⁹, 171, F₃, 54) (dual of [171, 42, 55]-code), using 1 times truncation based on linear OA(3¹³⁰, 172, F₃, 55) (dual of [172, 42, 56]-code), using

concatenation of two codes [i] based on
1. linear OA(27²⁹, 43, F₂₇, 27) (dual of [43, 14, 28]-code), using
  - discarding factors / shortening the dual code based on linear OA(27²⁹, 48, F₂₇, 27) (dual of [48, 19, 28]-code), using
    - extended algebraic-geometric code AG_e(F,20P) [i] based on function field F/F₂₇ with g(F) = 2 and N(F) ≥ 48, using
      - a function field by GarcÃa and Quoos [i]
2. linear OA(3¹, 4, F₃, 1) (dual of [4, 3, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 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(3¹²⁹, 85, F₃, 2, 54) (dual of [(85, 2), 41, 55]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3¹²⁹, 57, F₃, 3, 54) (dual of [(57, 3), 42, 55]-NRT-code)	[i]		OOA Folding