MinT - Information on Result #671941

Information on Result #671941

Linear OA(7⁷¹, 80, F₇, 48) (dual of [80, 9, 49]-code), using juxtaposition based on

linear OA(7²¹, 30, F₇, 14) (dual of [30, 9, 15]-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OA(7², 5, F₇, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,7)), using
    - discarding factors / shortening the dual code based on linear OA(7², 7, F₇, 2) (dual of [7, 5, 3]-code or 7-arc in PG(1,7)), using
      - Reedâ€“Solomon code RS(5,7) [i]
  2. linear OA(7², 5, F₇, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,7)) (see above)
  3. linear OA(7³, 5, F₇, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,7) or 5-cap in PG(2,7)), using
    - discarding factors / shortening the dual code based on linear OA(7³, 7, F₇, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,7) or 7-cap in PG(2,7)), using
      - Reedâ€“Solomon code RS(4,7) [i]
  4. linear OA(7⁴, 5, F₇, 4) (dual of [5, 1, 5]-code or 5-arc in PG(3,7)), using
    - dual of repetition code with length 5 [i]
  5. linear OA(7⁵, 5, F₇, 5) (dual of [5, 0, 6]-code or 5-arc in PG(4,7)), using
    - complete OA / dual of code with only one code word [i]
  6. linear OA(7⁵, 5, F₇, 5) (dual of [5, 0, 6]-code or 5-arc in PG(4,7)) (see above)
linear OA(7⁴¹, 50, F₇, 33) (dual of [50, 9, 34]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 50Â | 7⁴âˆ’1, defining interval IÂ =Â [0,16], and minimum distance dÂ â‰¥ |{−16,−15,…,16}|+1Â =Â 34 (BCH-bound) [i]

Mode: Constructive and linear.

None.

None.