MinT - Information on Result #941717

Information on Result #941717

Linear OOA(3¹⁷⁶, 90, F₃, 2, 136) (dual of [(90, 2), 4, 137]-NRT-code), using juxtaposition based on

linear OOA(3⁴, 4, F₃, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;4,3) [i]
linear OOA(3¹⁶⁸, 86, F₃, 2, 131) (dual of [(86, 2), 4, 132]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(3⁴, 4, F₃, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code) (see above)
  2. linear OOA(3¹⁶⁰, 82, F₃, 2, 126) (dual of [(82, 2), 4, 127]-NRT-code), using
    - juxtaposition [i] based on
      1. linear OOA(3⁴, 4, F₃, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code) (see above)
      2. linear OOA(3¹⁵², 78, F₃, 2, 121) (dual of [(78, 2), 4, 122]-NRT-code), using
        4 step truncation [i] based on linear OOA(3¹⁵⁶, 80, F₃, 2, 125) (dual of [(80, 2), 4, 126]-NRT-code), using
        concatenation of two NRT-codes [i] based on
        linear OA(9¹⁸, 20, F₉, 17) (dual of [20, 2, 18]-code), using
        repeating each code word 2 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]
        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(3¹⁷⁶, 90, F₃, 2, 135) (dual of [(90, 2), 4, 136]-NRT-code)	[i]		Strength Reduction for OOAs