MinT - Information on Result #896508

Information on Result #896508

Linear OOA(8⁶⁴, 4194366, F₈, 2, 9) (dual of [(4194366, 2), 8388668, 10]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8⁷, 65, F₈, 2, 4) (dual of [(65, 2), 123, 5]-NRT-code), using
- extracting embedded OOA [i] based on digital (3, 7, 65)-net over F₈, using
  - base reduction for projective spaces (embedding PG(3,64) in PG(6,8)) for nets [i] based on digital (0, 4, 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(8⁵⁷, 4194301, F₈, 2, 9) (dual of [(4194301, 2), 8388545, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8⁵⁷, 8388602, F₈, 9) (dual of [8388602, 8388545, 10]-code), using
  - discarding factors / shortening the dual code based on linear OA(8⁵⁷, large, F₈, 9) (dual of [large, large−57, 10]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 8⁸âˆ’1, defining interval IÂ =Â [0,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(8⁶⁴, 2097182, F₈, 10, 9) (dual of [(2097182, 10), 20971756, 10]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row