MinT - Information on Result #2230213

Information on Result #2230213

Linear OA(3¹⁰⁶, 163, F₃, 40) (dual of [163, 57, 41]-code), using 1 times truncation based on linear OA(3¹⁰⁷, 164, F₃, 41) (dual of [164, 57, 42]-code), using

concatenation of two codes [i] based on
1. linear OA(27²², 41, F₂₇, 20) (dual of [41, 19, 21]-code), using
  - discarding factors / shortening the dual code based on linear OA(27²², 48, F₂₇, 20) (dual of [48, 26, 21]-code), using
    - extended algebraic-geometric code AG_e(F,27P) [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(3¹⁰⁶, 81, F₃, 2, 40) (dual of [(81, 2), 56, 41]-NRT-code)	[i]		OOA Folding