MinT - Information on Result #2467948

Information on Result #2467948

Linear OOA(3²²¹, 215, F₃, 2, 68) (dual of [(215, 2), 209, 69]-NRT-code), using 1 step truncation based on linear OOA(3²²², 216, F₃, 2, 69) (dual of [(216, 2), 210, 70]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(27³⁸, 54, F₂₇, 2, 34) (dual of [(54, 2), 70, 35]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(27³⁸, 64, F₂₇, 2, 34) (dual of [(64, 2), 90, 35]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,93P) [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, 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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3²²¹, 107, F₃, 4, 68) (dual of [(107, 4), 207, 69]-NRT-code)	[i]		OOA Folding