MinT - Information on Result #896589

Information on Result #896589

Linear OOA(8¹²⁸, 4194366, F₈, 2, 17) (dual of [(4194366, 2), 8388604, 18]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8¹⁵, 65, F₈, 2, 8) (dual of [(65, 2), 115, 9]-NRT-code), using
- extracting embedded OOA [i] based on digital (7, 15, 65)-net over F₈, using
  - base reduction for projective spaces (embedding PG(7,64) in PG(14,8)) for nets [i] based on digital (0, 8, 65)-net over F₆₄, using
    - net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
        the rational function field F₆₄(x) [i]
      - Niederreiter sequence [i]
linear OOA(8¹¹³, 4194301, F₈, 2, 17) (dual of [(4194301, 2), 8388489, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8¹¹³, 8388602, F₈, 17) (dual of [8388602, 8388489, 18]-code), using
  - discarding factors / shortening the dual code based on linear OA(8¹¹³, large, F₈, 17) (dual of [large, large−113, 18]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 8¹⁶âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(8¹²⁸, 1048591, F₈, 18, 17) (dual of [(1048591, 18), 18874510, 18]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row