MinT - Information on Result #1525205

Information on Result #1525205

Linear OOA(3¹⁶⁴, 4194335, F₃, 3, 15) (dual of [(4194335, 3), 12582841, 16]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁶⁴, 4194335, F₃, 2, 15) (dual of [(4194335, 2), 8388506, 16]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3¹⁴, 34, F₃, 2, 7) (dual of [(34, 2), 54, 8]-NRT-code), using
  - extracting embedded OOA [i] based on digital (7, 14, 34)-net over F₃, using
    - linear code embedding found in a computer search [i]
2. linear OOA(3¹⁵⁰, 4194301, F₃, 2, 15) (dual of [(4194301, 2), 8388452, 16]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3¹⁵⁰, 8388602, F₃, 15) (dual of [8388602, 8388452, 16]-code), using
    - discarding factors / shortening the dual code based on linear OA(3¹⁵⁰, large, F₃, 15) (dual of [large, large−150, 16]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [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(3¹⁶⁵, 4194335, F₃, 3, 15) (dual of [(4194335, 3), 12582840, 16]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(3¹⁶⁴, 2097167, F₃, 5, 15) (dual of [(2097167, 5), 10485671, 16]-NRT-code)	[i]		OOA Folding