MinT - Information on Result #1027652

Information on Result #1027652

Linear OOA(5¹⁴⁹, 51, F₅, 3, 132) (dual of [(51, 3), 4, 133]-NRT-code), using juxtaposition based on

linear OOA(5²⁶, 10, F₅, 3, 25) (dual of [(10, 3), 4, 26]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,4P) [i] based on function field F/F₅ with g(F) = 1 and N(F) ≥ 10, using
  - an explicitly constructive algebraic function field [i]
linear OOA(5¹¹⁹, 41, F₅, 3, 106) (dual of [(41, 3), 4, 107]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(5²³, 9, F₅, 3, 22) (dual of [(9, 3), 4, 23]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(5²³, 10, F₅, 3, 22) (dual of [(10, 3), 7, 23]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,7P) [i] based on function field F/F₅ with g(F) = 1 and N(F) ≥ 10 (see above)
  2. linear OOA(5⁹², 32, F₅, 3, 83) (dual of [(32, 3), 4, 84]-NRT-code), using
    - repeating each code word 2 times [i] based on linear OOA(5⁴⁴, 16, F₅, 3, 41) (dual of [(16, 3), 4, 42]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,6P) [i] based on function field F/F₅ with g(F) = 3 and N(F) ≥ 16, using
        an explicitly constructive algebraic function field [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(5¹⁴⁴, 49, F₅, 3, 127) (dual of [(49, 3), 3, 128]-NRT-code)	[i]		Truncation for OOAs