MinT - Information on Result #1523162

Information on Result #1523162

Linear OOA(3¹²⁹, 4194314, F₃, 3, 12) (dual of [(4194314, 3), 12582813, 13]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹²⁹, 4194314, F₃, 2, 12) (dual of [(4194314, 2), 8388499, 13]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3⁹, 13, F₃, 2, 6) (dual of [(13, 2), 17, 7]-NRT-code), using
  - extracting embedded OOA [i] based on digital (3, 9, 13)-net over F₃, using
    - linear code embedding found in a computer search [i]
2. linear OOA(3¹²⁰, 4194301, F₃, 2, 12) (dual of [(4194301, 2), 8388482, 13]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3¹²⁰, 8388602, F₃, 12) (dual of [8388602, 8388482, 13]-code), using
    - discarding factors / shortening the dual code based on linear OA(3¹²⁰, large, F₃, 12) (dual of [large, large−120, 13]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [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(3¹²⁹, 2097157, F₃, 5, 12) (dual of [(2097157, 5), 10485656, 13]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3¹²⁹, 2097156, F₃, 15, 12) (dual of [(2097156, 15), 31457211, 13]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row