MinT - Information on Result #2495230

Information on Result #2495230

Linear OOA(4¹⁷⁸, 4195330, F₄, 2, 16) (dual of [(4195330, 2), 8390482, 17]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(4¹⁷⁶, 4195329, F₄, 2, 16) (dual of [(4195329, 2), 8390482, 17]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(4³², 1028, F₄, 2, 8) (dual of [(1028, 2), 2024, 9]-NRT-code), using
  - extracting embedded OOA [i] based on digital (24, 32, 1028)-net over F₄, using
    - trace code 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]
2. 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.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(4¹⁷⁹, 4195330, F₄, 2, 16) (dual of [(4195330, 2), 8390481, 17]-NRT-code)	[i]		OOA Duplication