MinT - Information on Result #941837

Information on Result #941837

Linear OOA(3²⁰¹, 102, F₃, 2, 160) (dual of [(102, 2), 3, 161]-NRT-code), using juxtaposition based on

linear OOA(3¹¹, 7, F₃, 2, 10) (dual of [(7, 2), 3, 11]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,3P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
  - an explicitly constructive algebraic function field [i]
linear OOA(3¹⁸⁷, 95, F₃, 2, 149) (dual of [(95, 2), 3, 150]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(3¹¹, 7, F₃, 2, 10) (dual of [(7, 2), 3, 11]-NRT-code) (see above)
  2. linear OOA(3¹⁷³, 88, F₃, 2, 138) (dual of [(88, 2), 3, 139]-NRT-code), using
    - juxtaposition [i] based on
      1. linear OOA(3⁹, 6, F₃, 2, 8) (dual of [(6, 2), 3, 9]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(3⁹, 7, F₃, 2, 8) (dual of [(7, 2), 5, 9]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(2;F,5P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7 (see above)
      2. linear OOA(3¹⁶¹, 82, F₃, 2, 129) (dual of [(82, 2), 3, 130]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(3⁵, 4, F₃, 2, 5) (dual of [(4, 2), 3, 6]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;3,3) [i]
        linear OOA(3¹⁵³, 78, F₃, 2, 123) (dual of [(78, 2), 3, 124]-NRT-code), using
        repeating each code word 2 times [i] based on linear OOA(3⁷⁵, 39, F₃, 2, 61) (dual of [(39, 2), 3, 62]-NRT-code), using
        1 step truncation [i] based on linear OOA(3⁷⁶, 40, F₃, 2, 62) (dual of [(40, 2), 4, 63]-NRT-code), using
        concatenation of two NRT-codes [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]
        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(3²¹⁵, 109, F₃, 2, 171) (dual of [(109, 2), 3, 172]-NRT-code)	[i]		Juxtaposition for OOAs
2	Linear OOA(3²⁰¹, 51, F₃, 4, 160) (dual of [(51, 4), 3, 161]-NRT-code)	[i]		OOA Folding