MinT - Information on Result #1605784

Information on Result #1605784

Linear OOA(3¹⁶¹, 4194316, F₃, 4, 15) (dual of [(4194316, 4), 16777103, 16]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁶¹, 4194316, F₃, 2, 15) (dual of [(4194316, 2), 8388471, 16]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3¹¹, 15, F₃, 2, 7) (dual of [(15, 2), 19, 8]-NRT-code), using
  - extracting embedded OOA [i] based on digital (4, 11, 15)-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(3¹⁶¹, 2097157, F₃, 20, 15) (dual of [(2097157, 20), 41942979, 16]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row