MinT - Information on Result #910011

Information on Result #910011

Linear OOA(5¹²⁷, 66, F₅, 2, 102) (dual of [(66, 2), 5, 103]-NRT-code), using juxtaposition based on

linear OOA(5⁷, 6, F₅, 2, 7) (dual of [(6, 2), 5, 8]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;5,5) [i]
linear OOA(5¹¹⁵, 60, F₅, 2, 94) (dual of [(60, 2), 5, 95]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(5²⁰, 12, F₅, 2, 18) (dual of [(12, 2), 4, 19]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,5P) [i] based on function field F/F₅ with g(F) = 2 and N(F) ≥ 12, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(5²³, 12, F₅, 2, 23) (dual of [(12, 2), 1, 24]-NRT-code), using
    - dual of repetition NRT-code with length 12 [i]
  3. linear OOA(5²⁴, 12, F₅, 2, 24) (dual of [(12, 2), 0, 25]-NRT-code), using
    - complete OOA / dual of NRT-code with only one code word [i]
  4. linear OOA(5²⁴, 12, F₅, 2, 24) (dual of [(12, 2), 0, 25]-NRT-code) (see above)
  5. linear OOA(5²⁴, 12, F₅, 2, 24) (dual of [(12, 2), 0, 25]-NRT-code) (see above)

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(5¹²⁷, 66, F₅, 2, 101) (dual of [(66, 2), 5, 102]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(5¹²⁷, 66, F₅, 2, 100) (dual of [(66, 2), 5, 101]-NRT-code)	[i]		Strength Reduction for OOAs