MinT - Information on Result #1606797

Information on Result #1606797

Linear OOA(3¹⁷⁶, 4194418, F₃, 4, 16) (dual of [(4194418, 4), 16777496, 17]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁷⁶, 4194418, F₃, 2, 16) (dual of [(4194418, 2), 8388660, 17]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3²⁵, 117, F₃, 2, 8) (dual of [(117, 2), 209, 9]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3²⁵, 117, F₃, 8) (dual of [117, 92, 9]-code), using
    - discarding factors / shortening the dual code based on linear OA(3²⁵, 121, F₃, 8) (dual of [121, 96, 9]-code), using
      - the BCH-code C(I) with length 121Â | 3⁵âˆ’1, defining interval IÂ =Â {1,3,5,…,15}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
2. linear OOA(3¹⁵¹, 4194301, F₃, 2, 16) (dual of [(4194301, 2), 8388451, 17]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3¹⁵¹, 8388602, F₃, 16) (dual of [8388602, 8388451, 17]-code), using
    - discarding factors / shortening the dual code based on linear OA(3¹⁵¹, large, F₃, 16) (dual of [large, large−151, 17]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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(3¹⁷⁶, 2097208, F₃, 20, 16) (dual of [(2097208, 20), 41943984, 17]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row