MinT - Information on Result #2628105

Information on Result #2628105

Linear OOA(3²³³, 111, F₃, 3, 106) (dual of [(111, 3), 100, 107]-NRT-code), using strength reduction based on linear OOA(3²³³, 111, F₃, 3, 107) (dual of [(111, 3), 100, 108]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(9⁶¹, 37, F₉, 3, 53) (dual of [(37, 3), 50, 54]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(9⁶¹, 39, F₉, 3, 53) (dual of [(39, 3), 56, 54]-NRT-code), using
    - algebraic-geometric NRT-code AG(3;F,63P) [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [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(3²³⁴, 111, F₃, 3, 106) (dual of [(111, 3), 99, 107]-NRT-code)	[i]		OOA Duplication