MinT - Information on Result #1193281

Information on Result #1193281

Linear OOA(9⁶³, 1195782, F₉, 10, 9) (dual of [(1195782, 10), 11957757, 10]-NRT-code), using OOA 2-folding and stacking with additional row based on linear OOA(9⁶³, 2391565, F₉, 2, 9) (dual of [(2391565, 2), 4783067, 10]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(9⁶³, 2391566, F₉, 2, 9) (dual of [(2391566, 2), 4783069, 10]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(9⁷, 82, F₉, 2, 4) (dual of [(82, 2), 157, 5]-NRT-code), using
    - extracting embedded OOA [i] based on digital (3, 7, 82)-net over F₉, using
      - base reduction for projective spaces (embedding PG(3,81) in PG(6,9)) for nets [i] based on digital (0, 4, 82)-net over F₈₁, using
        net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
        the rational function field F₈₁(x) [i]
        Niederreiter sequence [i]
  2. linear OOA(9⁵⁶, 2391484, F₉, 2, 9) (dual of [(2391484, 2), 4782912, 10]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(9⁵⁶, 4782968, F₉, 9) (dual of [4782968, 4782912, 10]-code), using
      - 1 times truncation [i] based on linear OA(9⁵⁷, 4782969, F₉, 10) (dual of [4782969, 4782912, 11]-code), using
        an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]

Mode: Constructive and linear.

Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (54, 63, 1195782)-net over F₉	[i]		Net Defined by OOA