MinT - Information on Result #910023

Information on Result #910023

Linear OOA(5¹²⁵, 65, F₅, 2, 102) (dual of [(65, 2), 5, 103]-NRT-code), using juxtaposition based on

linear OOA(5²⁵, 15, F₅, 2, 22) (dual of [(15, 2), 5, 23]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(5²⁵, 16, F₅, 2, 22) (dual of [(16, 2), 7, 23]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,9P) [i] based on function field F/F₅ with g(F) = 3 and N(F) ≥ 16, using
    - an explicitly constructive algebraic function field [i]
linear OOA(5⁹⁵, 50, F₅, 2, 79) (dual of [(50, 2), 5, 80]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(5¹⁶, 10, F₅, 2, 15) (dual of [(10, 2), 4, 16]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;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]
  2. linear OOA(5¹⁹, 10, F₅, 2, 19) (dual of [(10, 2), 1, 20]-NRT-code), using
    - dual of repetition NRT-code with length 10 [i]
  3. linear OOA(5²⁰, 10, F₅, 2, 20) (dual of [(10, 2), 0, 21]-NRT-code), using
    - complete OOA / dual of NRT-code with only one code word [i]
  4. linear OOA(5²⁰, 10, F₅, 2, 20) (dual of [(10, 2), 0, 21]-NRT-code) (see above)
  5. linear OOA(5²⁰, 10, F₅, 2, 20) (dual of [(10, 2), 0, 21]-NRT-code) (see above)

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(5¹²⁵, 65, F₅, 2, 101) (dual of [(65, 2), 5, 102]-NRT-code)	[i]		Strength Reduction for OOAs