MinT - Information on Result #2229873

Information on Result #2229873

Linear OA(3¹¹², 139, F₃, 50) (dual of [139, 27, 51]-code), using 1 times truncation based on linear OA(3¹¹³, 140, F₃, 51) (dual of [140, 27, 52]-code), using

concatenation of two codes [i] based on
1. linear OA(27²⁶, 35, F₂₇, 25) (dual of [35, 9, 26]-code), using
  - discarding factors / shortening the dual code based on linear OA(27²⁶, 38, F₂₇, 25) (dual of [38, 12, 26]-code), using
    - extended algebraic-geometric code AG_e(F,12P) [i] based on function field F/F₂₇ with g(F) = 1 and N(F) ≥ 38, using
      - a function field by SÃ©mirat [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(3¹¹², 69, F₃, 2, 50) (dual of [(69, 2), 26, 51]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3¹¹², 46, F₃, 3, 50) (dual of [(46, 3), 26, 51]-NRT-code)	[i]		OOA Folding