MinT - Information on Result #1607824

Information on Result #1607824

Linear OOA(3¹⁹⁰, 4194397, F₃, 4, 17) (dual of [(4194397, 4), 16777398, 18]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁹⁰, 4194397, F₃, 2, 17) (dual of [(4194397, 2), 8388604, 18]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3²⁴, 96, F₃, 2, 8) (dual of [(96, 2), 168, 9]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3²⁴, 96, F₃, 8) (dual of [96, 72, 9]-code), using
    - discarding factors / shortening the dual code based on linear OA(3²⁴, 99, F₃, 8) (dual of [99, 75, 9]-code), using
      - a â€œXBâ€ code from Brouwerâ€™s database [i]
2. linear OOA(3¹⁶⁶, 4194301, F₃, 2, 17) (dual of [(4194301, 2), 8388436, 18]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3¹⁶⁶, 8388602, F₃, 17) (dual of [8388602, 8388436, 18]-code), using
    - discarding factors / shortening the dual code based on linear OA(3¹⁶⁶, large, F₃, 17) (dual of [large, large−166, 18]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [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(3¹⁹⁰, 2097198, F₃, 20, 17) (dual of [(2097198, 20), 41943770, 18]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row