MinT - Information on Result #2661589

Information on Result #2661589

Linear OOA(3²²⁶, 104, F₃, 3, 108) (dual of [(104, 3), 86, 109]-NRT-code), using 1 step truncation based on linear OOA(3²²⁷, 105, F₃, 3, 109) (dual of [(105, 3), 88, 110]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(9⁶¹, 35, F₉, 3, 54) (dual of [(35, 3), 44, 55]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(9⁶¹, 36, F₉, 3, 54) (dual of [(36, 3), 47, 55]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,53P) [i] based on function field F/F₉ with g(F) = 7 and N(F) ≥ 36, 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(3²²⁶, 52, F₃, 5, 108) (dual of [(52, 5), 34, 109]-NRT-code)	[i]		OOA Folding