MinT - Information on Result #909161

Information on Result #909161

Linear OOA(3⁴⁵, 25, F₃, 2, 32) (dual of [(25, 2), 5, 33]-NRT-code), using juxtaposition 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, using
  - an explicitly constructive algebraic function field [i]
linear OOA(3³¹, 18, F₃, 2, 23) (dual of [(18, 2), 5, 24]-NRT-code), using
- generalized (u,Â u+v)-construction [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 (see above)
  2. linear OOA(3¹¹, 6, F₃, 2, 11) (dual of [(6, 2), 1, 12]-NRT-code), using
    - dual of repetition NRT-code with length 6 [i]
  3. linear OOA(3¹², 6, F₃, 2, 12) (dual of [(6, 2), 0, 13]-NRT-code), using
    - complete OOA / dual of NRT-code with only one code word [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3⁴⁵, 25, F₃, 2, 31) (dual of [(25, 2), 5, 32]-NRT-code)	[i]		Strength Reduction for OOAs