MinT - Information on Result #2626390

Information on Result #2626390

Linear OOA(3²⁰⁶, 76, F₃, 3, 133) (dual of [(76, 3), 22, 134]-NRT-code), using strength reduction based on linear OOA(3²⁰⁶, 76, F₃, 3, 134) (dual of [(76, 3), 22, 135]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(9⁴⁶, 19, F₉, 3, 44) (dual of [(19, 3), 11, 45]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(9⁴⁶, 20, F₉, 3, 44) (dual of [(20, 3), 14, 45]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,15P) [i] based on function field F/F₉ with g(F) = 2 and N(F) ≥ 20, using
      - a function field by GarcÃa and Quoos [i]
2. linear OA(3², 4, F₃, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,3)), using
  - extended Reedâ€“Solomon code RS_e(2,3) [i]
  - Hamming code H(2,3) [i]
  - Simplex code S(2,3) [i]
  - the Tetracode [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(3²⁰⁵, 75, F₃, 3, 132) (dual of [(75, 3), 20, 133]-NRT-code)	[i]		Truncation for OOAs