MinT - Information on Result #2462110

Information on Result #2462110

Linear OOA(3⁷⁸, 41, F₃, 2, 57) (dual of [(41, 2), 4, 58]-NRT-code), using 22 step truncation based on linear OOA(3¹⁰⁰, 52, F₃, 2, 79) (dual of [(52, 2), 4, 80]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(3²⁰, 12, F₃, 2, 16) (dual of [(12, 2), 4, 17]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,7P) [i] based on function field F/F₃ with g(F) = 4 and N(F) ≥ 12, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(3⁷⁶, 40, F₃, 2, 62) (dual of [(40, 2), 4, 63]-NRT-code), using
  - concatenation of two NRT-codes [i] based on
    1. linear OA(9⁸, 10, F₉, 8) (dual of [10, 2, 9]-code or 10-arc in PG(7,9)), using
      - extended Reedâ€“Solomon code RS_e(2,9) [i]
      - Simplex code S(2,9) [i]
    2. linear OOA(3⁶, 4, F₃, 2, 6) (dual of [(4, 2), 2, 7]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(2;2,3) [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(3⁸⁶, 45, F₃, 2, 62) (dual of [(45, 2), 4, 63]-NRT-code)	[i]		Juxtaposition for OOAs