MinT - Information on Result #2495364

Information on Result #2495364

Linear OOA(4¹⁷¹, 4194497, F₄, 2, 17) (dual of [(4194497, 2), 8388823, 18]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(4¹⁶⁹, 4194496, F₄, 2, 17) (dual of [(4194496, 2), 8388823, 18]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(4²⁴, 195, F₄, 2, 8) (dual of [(195, 2), 366, 9]-NRT-code), using
  - extracting embedded OOA [i] based on digital (16, 24, 195)-net over F₄, using
    - trace code for nets [i] based on digital (0, 8, 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]
2. linear OOA(4¹⁴⁵, 4194301, F₄, 2, 17) (dual of [(4194301, 2), 8388457, 18]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(4¹⁴⁵, 8388602, F₄, 17) (dual of [8388602, 8388457, 18]-code), using
    - discarding factors / shortening the dual code based on linear OA(4¹⁴⁵, large, F₄, 17) (dual of [large, large−145, 18]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 4²⁴âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [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(4¹⁷¹, 1048624, F₄, 18, 17) (dual of [(1048624, 18), 18875061, 18]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row