MinT - Information on Result #813264

Information on Result #813264

Linear OOA(3¹⁰⁹, 29543, F₃, 2, 16) (dual of [(29543, 2), 58977, 17]-NRT-code), using OOA 2-folding based on linear OA(3¹⁰⁹, 59086, F₃, 16) (dual of [59086, 58977, 17]-code), using

discarding factors / shortening the dual code based on linear OA(3¹⁰⁹, 59087, F₃, 16) (dual of [59087, 58978, 17]-code), using
- constructionÂ X applied to C_e(15) âŠ‚ C_e(10) [i] based on
  1. linear OA(3¹⁰¹, 59049, F₃, 16) (dual of [59049, 58948, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
  2. linear OA(3⁷¹, 59049, F₃, 11) (dual of [59049, 58978, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
  3. linear OA(3⁸, 38, F₃, 4) (dual of [38, 30, 5]-code), using
    - discarding factors / shortening the dual code based on linear OA(3⁸, 41, F₃, 4) (dual of [41, 33, 5]-code), using
      - the narrow-sense BCH-code C(I) with length 41Â | 3⁸âˆ’1, defining interval IÂ =Â [1,1], and minimum distance dÂ â‰¥ |{−3,−1,1,3}|+1Â =Â 5 (BCH-bound) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OOA(3¹⁰⁹, 23946, F₃, 3, 16) (dual of [(23946, 3), 71729, 17]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹⁰⁹, 23946, F₃, 4, 16) (dual of [(23946, 4), 95675, 17]-NRT-code)	[i]
3	Linear OOA(3¹⁰⁹, 23946, F₃, 5, 16) (dual of [(23946, 5), 119621, 17]-NRT-code)	[i]
4	Digital (93, 109, 23946)-net over F₃	[i]