MinT - Information on Result #941798

Information on Result #941798

Linear OOA(3²⁴⁹, 126, F₃, 2, 198) (dual of [(126, 2), 3, 199]-NRT-code), using juxtaposition based on

linear OOA(3⁷, 5, F₃, 2, 6) (dual of [(5, 2), 3, 7]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3⁷, 7, F₃, 2, 6) (dual of [(7, 2), 7, 7]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,7P) [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(3²³⁹, 121, F₃, 2, 191) (dual of [(121, 2), 3, 192]-NRT-code), using
- juxtaposition [i] based on
  1. 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]
  2. linear OOA(3²³¹, 117, F₃, 2, 185) (dual of [(117, 2), 3, 186]-NRT-code), using
    - repeating each code word 3 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.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3²⁴⁸, 125, F₃, 2, 197) (dual of [(125, 2), 2, 198]-NRT-code)	[i]		Truncation for OOAs
2	Linear OOA(3²⁴⁹, 63, F₃, 4, 198) (dual of [(63, 4), 3, 199]-NRT-code)	[i]		OOA Folding