MinT - Information on Result #909203

Information on Result #909203

Linear OOA(3²⁰⁷, 106, F₃, 2, 141) (dual of [(106, 2), 5, 142]-NRT-code), using juxtaposition based on

linear OOA(3¹⁹, 12, F₃, 2, 15) (dual of [(12, 2), 5, 16]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,8P) [i] based on function field F/F₃ with g(F) = 4 and N(F) ≥ 12, using
  - an explicitly constructive algebraic function field [i]
linear OOA(3¹⁸³, 94, F₃, 2, 125) (dual of [(94, 2), 5, 126]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(3¹⁹, 12, F₃, 2, 15) (dual of [(12, 2), 5, 16]-NRT-code) (see above)
  2. linear OOA(3¹⁵⁹, 82, F₃, 2, 109) (dual of [(82, 2), 5, 110]-NRT-code), using
    - juxtaposition [i] based on
      1. linear OOA(3¹⁹, 12, F₃, 2, 15) (dual of [(12, 2), 5, 16]-NRT-code) (see above)
      2. linear OOA(3¹³⁵, 70, F₃, 2, 93) (dual of [(70, 2), 5, 94]-NRT-code), using
        repeating each code word 2 times [i] based on linear OOA(3⁶⁵, 35, F₃, 2, 46) (dual of [(35, 2), 5, 47]-NRT-code), using
        9 step truncation [i] based on linear OOA(3⁷⁴, 40, F₃, 2, 55) (dual of [(40, 2), 6, 56]-NRT-code), using
        concatenation of two NRT-codes [i] based on
        linear OA(9⁷, 10, F₉, 7) (dual of [10, 3, 8]-code or 10-arc in PG(6,9)), using
        extended Reedâ€“Solomon code RS_e(3,9) [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(3²³¹, 118, F₃, 2, 157) (dual of [(118, 2), 5, 158]-NRT-code)	[i]		Juxtaposition for OOAs