MinT - Information on Result #1014381

Information on Result #1014381

Linear OOA(8⁹¹, 5592467, F₈, 3, 11) (dual of [(5592467, 3), 16777310, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8⁹, 65, F₈, 3, 5) (dual of [(65, 3), 186, 6]-NRT-code), using
- extracting embedded OOA [i] based on digital (4, 9, 65)-net over F₈, using
  - base reduction for projective spaces (embedding PG(4,64) in PG(8,8)) for nets [i] based on digital (0, 5, 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(8⁸², 5592402, F₈, 3, 11) (dual of [(5592402, 3), 16777124, 12]-NRT-code), using
- trace code [i] based on linear OOA(64⁴¹, 2796201, F₆₄, 3, 11) (dual of [(2796201, 3), 8388562, 12]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(64⁴¹, large, F₆₄, 11) (dual of [large, large−41, 12]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(8⁹¹, 2796233, F₈, 15, 11) (dual of [(2796233, 15), 41943404, 12]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row