MinT - Information on Result #2434664

Information on Result #2434664

Linear OOA(3¹⁹², 168, F₃, 2, 68) (dual of [(168, 2), 144, 69]-NRT-code), using strength reduction based on linear OOA(3¹⁹², 168, F₃, 2, 69) (dual of [(168, 2), 144, 70]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(27³⁶, 42, F₂₇, 2, 34) (dual of [(42, 2), 48, 35]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(27³⁶, 48, F₂₇, 2, 34) (dual of [(48, 2), 60, 35]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,61P) [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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3¹⁹², 84, F₃, 4, 68) (dual of [(84, 4), 144, 69]-NRT-code)	[i]		OOA Folding