MinT - Information on Result #2467732

Information on Result #2467732

Linear OOA(3²¹¹, 171, F₃, 2, 80) (dual of [(171, 2), 131, 81]-NRT-code), using 1 step truncation based on linear OOA(3²¹², 172, F₃, 2, 81) (dual of [(172, 2), 132, 82]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(27⁴², 43, F₂₇, 2, 40) (dual of [(43, 2), 44, 41]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(27⁴², 48, F₂₇, 2, 40) (dual of [(48, 2), 54, 41]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,55P) [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(3²¹¹, 85, F₃, 4, 80) (dual of [(85, 4), 129, 81]-NRT-code)	[i]		OOA Folding