MinT - Information on Result #1529814

Information on Result #1529814

Linear OOA(3²¹⁷, 4194706, F₃, 3, 19) (dual of [(4194706, 3), 12583901, 20]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²¹⁷, 4194706, F₃, 2, 19) (dual of [(4194706, 2), 8389195, 20]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3³⁶, 405, F₃, 2, 9) (dual of [(405, 2), 774, 10]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3³⁶, 405, F₃, 9) (dual of [405, 369, 10]-code), using
    - discarding factors / shortening the dual code based on linear OA(3³⁶, 728, F₃, 9) (dual of [728, 692, 10]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
2. linear OOA(3¹⁸¹, 4194301, F₃, 2, 19) (dual of [(4194301, 2), 8388421, 20]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3¹⁸¹, 8388602, F₃, 19) (dual of [8388602, 8388421, 20]-code), using
    - discarding factors / shortening the dual code based on linear OA(3¹⁸¹, large, F₃, 19) (dual of [large, large−181, 20]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 3³⁰âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [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(3²¹⁷, 2097353, F₃, 5, 19) (dual of [(2097353, 5), 10486548, 20]-NRT-code)	[i]		OOA Folding