MinT - Information on Result #1648059

Information on Result #1648059

Linear OOA(3¹⁹⁹, 4194327, F₃, 5, 18) (dual of [(4194327, 5), 20971436, 19]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁹⁹, 4194327, F₃, 2, 18) (dual of [(4194327, 2), 8388455, 19]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3¹⁹, 26, F₃, 2, 9) (dual of [(26, 2), 33, 10]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(3⁶, 14, F₃, 2, 4) (dual of [(14, 2), 22, 5]-NRT-code), using
      - extracting embedded OOA [i] based on digital (2, 6, 14)-net over F₃, using
        linear code embedding found in a computer search [i]
    2. linear OOA(3¹³, 13, F₃, 2, 9) (dual of [(13, 2), 13, 10]-NRT-code), using
      - extracting embedded OOA [i] based on digital (4, 13, 13)-net over F₃, using
        a shift-net [i]
2. linear OOA(3¹⁸⁰, 4194301, F₃, 2, 18) (dual of [(4194301, 2), 8388422, 19]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3¹⁸⁰, 8388602, F₃, 18) (dual of [8388602, 8388422, 19]-code), using
    - discarding factors / shortening the dual code based on linear OA(3¹⁸⁰, large, F₃, 18) (dual of [large, large−180, 19]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [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(3¹⁹⁹, 2097163, F₃, 25, 18) (dual of [(2097163, 25), 52428876, 19]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row