MinT - Information on Result #910059

Information on Result #910059

Linear OOA(5¹¹⁴, 59, F₅, 2, 94) (dual of [(59, 2), 4, 95]-NRT-code), using juxtaposition based on

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]
linear OOA(5⁹⁴, 49, F₅, 2, 78) (dual of [(49, 2), 4, 79]-NRT-code), using
- 1 step truncation [i] based on 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) (see above)
    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(5¹¹⁴, 59, F₅, 2, 93) (dual of [(59, 2), 4, 94]-NRT-code)	[i]		Strength Reduction for OOAs