MinT - Information on Result #1606517

Information on Result #1606517

Linear OOA(3¹⁷², 4194355, F₃, 4, 16) (dual of [(4194355, 4), 16777248, 17]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁷², 4194355, F₃, 2, 16) (dual of [(4194355, 2), 8388538, 17]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3²¹, 54, F₃, 2, 8) (dual of [(54, 2), 87, 9]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3²¹, 54, F₃, 8) (dual of [54, 33, 9]-code), using
    - discarding factors / shortening the dual code based on linear OA(3²¹, 80, F₃, 8) (dual of [80, 59, 9]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 80Â = 3⁴âˆ’1, defining interval IÂ =Â [0,7], 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(3¹⁷², 2097177, F₃, 20, 16) (dual of [(2097177, 20), 41943368, 17]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row