MinT - Information on Result #1612404

Information on Result #1612404

Linear OOA(3²⁴², 2796214, F₃, 4, 23) (dual of [(2796214, 4), 11184614, 24]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²⁴², 2796214, F₃, 3, 23) (dual of [(2796214, 3), 8388400, 24]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3¹⁶, 13, F₃, 3, 11) (dual of [(13, 3), 23, 12]-NRT-code), using
  - extracting embedded OOA [i] based on digital (5, 16, 13)-net over F₃, using
    - net from sequence [i] based on digital (5, 12)-sequence over F₃, using
      - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₃ with g(F)Â =Â 4, N(F)Â =Â 12, and 1 place with degree 2 [i] based on function field F/F₃ with g(F) = 4 and N(F) ≥ 12, using an explicitly constructive algebraic function field [i]
2. linear OOA(3²²⁶, 2796201, F₃, 3, 23) (dual of [(2796201, 3), 8388377, 24]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(3²²⁶, large, F₃, 23) (dual of [large, large−226, 24]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 24 [i]

Mode: 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(3²⁴², 932071, F₃, 28, 23) (dual of [(932071, 28), 26097746, 24]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row