MinT - Information on Result #2438158

Information on Result #2438158

Linear OOA(3²⁴⁸, 126, F₃, 2, 195) (dual of [(126, 2), 4, 196]-NRT-code), using strength reduction based on linear OOA(3²⁴⁸, 126, F₃, 2, 196) (dual of [(126, 2), 4, 197]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(3⁸, 6, F₃, 2, 7) (dual of [(6, 2), 4, 8]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(3⁸, 7, F₃, 2, 7) (dual of [(7, 2), 6, 8]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,6P) [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(3²³⁶, 120, F₃, 2, 188) (dual of [(120, 2), 4, 189]-NRT-code), using
  - concatenation of two NRT-codes [i] based on
    1. linear OA(9²⁸, 30, F₉, 26) (dual of [30, 2, 27]-code), using
      - repeating each code word 3 times [i] based on 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(3²⁴⁸, 63, F₃, 4, 195) (dual of [(63, 4), 4, 196]-NRT-code)	[i]		OOA Folding