MinT - Information on Result #2629139

Information on Result #2629139

Linear OOA(3²⁵⁰, 85, F₃, 3, 199) (dual of [(85, 3), 5, 200]-NRT-code), using strength reduction based on linear OOA(3²⁵⁰, 85, F₃, 3, 200) (dual of [(85, 3), 5, 201]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(3¹³, 6, F₃, 3, 12) (dual of [(6, 3), 5, 13]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(3¹³, 7, F₃, 3, 12) (dual of [(7, 3), 8, 13]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,8P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
      - an explicitly constructive algebraic function field [i]
2. linear OOA(3²³², 79, F₃, 3, 187) (dual of [(79, 3), 5, 188]-NRT-code), using
  - 2 step truncation [i] based on linear OOA(3²³⁴, 80, F₃, 3, 189) (dual of [(80, 3), 6, 190]-NRT-code), using
    - concatenation of two NRT-codes [i] based on
      1. linear OA(27¹⁸, 20, F₂₇, 18) (dual of [20, 2, 19]-code or 20-arc in PG(17,27)), using
        discarding factors / shortening the dual code based on linear OA(27¹⁸, 27, F₂₇, 18) (dual of [27, 9, 19]-code or 27-arc in PG(17,27)), using
        Reedâ€“Solomon code RS(9,27) [i]
      2. linear OOA(3⁹, 4, F₃, 3, 9) (dual of [(4, 3), 3, 10]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(3;3,3) [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(3²⁴⁷, 84, F₃, 3, 196) (dual of [(84, 3), 5, 197]-NRT-code)	[i]		Truncation for OOAs