MinT - Information on Result #2467829

Information on Result #2467829

Linear OOA(3²³⁹, 170, F₃, 2, 100) (dual of [(170, 2), 101, 101]-NRT-code), using 1 step truncation based on linear OOA(3²⁴⁰, 171, F₃, 2, 101) (dual of [(171, 2), 102, 102]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(9⁶³, 57, F₉, 2, 50) (dual of [(57, 2), 51, 51]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(9⁶³, 63, F₉, 2, 50) (dual of [(63, 2), 63, 51]-NRT-code), using
    - algebraic-geometric NRT-code AG(2;F,75P) [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]
2. linear OA(3¹, 3, F₃, 1) (dual of [3, 2, 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(3²³⁹, 85, F₃, 4, 100) (dual of [(85, 4), 101, 101]-NRT-code)	[i]		OOA Folding