MinT - Information on Result #895589

Information on Result #895589

Linear OOA(4¹⁷³, 4194558, F₄, 2, 16) (dual of [(4194558, 2), 8388943, 17]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(4²⁹, 257, F₄, 2, 8) (dual of [(257, 2), 485, 9]-NRT-code), using
- extracting embedded OOA [i] based on digital (21, 29, 257)-net over F₄, using
  - base reduction for projective spaces (embedding PG(7,256) in PG(28,4)) for nets [i] based on digital (0, 8, 257)-net over F₂₅₆, using
    - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
        the rational function field F₂₅₆(x) [i]
      - Niederreiter sequence [i]
linear OOA(4¹⁴⁴, 4194301, F₄, 2, 16) (dual of [(4194301, 2), 8388458, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4¹⁴⁴, 8388602, F₄, 16) (dual of [8388602, 8388458, 17]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹⁴⁴, large, F₄, 16) (dual of [large, large−144, 17]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(4¹⁷³, 1048639, F₄, 18, 16) (dual of [(1048639, 18), 18875329, 17]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row