MinT - Information on Result #2230982

Information on Result #2230982

Linear OA(3¹³¹, 167, F₃, 56) (dual of [167, 36, 57]-code), using 1 times truncation based on linear OA(3¹³², 168, F₃, 57) (dual of [168, 36, 58]-code), using

concatenation of two codes [i] based on
1. linear OA(27³⁰, 42, F₂₇, 28) (dual of [42, 12, 29]-code), using
  - discarding factors / shortening the dual code based on linear OA(27³⁰, 48, F₂₇, 28) (dual of [48, 18, 29]-code), using
    - extended algebraic-geometric code AG_e(F,19P) [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(3¹³¹, 83, F₃, 2, 56) (dual of [(83, 2), 35, 57]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3¹³¹, 55, F₃, 3, 56) (dual of [(55, 3), 34, 57]-NRT-code)	[i]		OOA Folding