MinT - Information on Result #984801

Information on Result #984801

Linear OOA(9⁹⁹, 1594325, F₉, 3, 16) (dual of [(1594325, 3), 4782876, 17]-NRT-code), using OOA 3-folding based on linear OA(9⁹⁹, 4782975, F₉, 16) (dual of [4782975, 4782876, 17]-code), using

discarding factors / shortening the dual code based on linear OA(9⁹⁹, 4782976, F₉, 16) (dual of [4782976, 4782877, 17]-code), using
- constructionÂ X applied to C_e(15) âŠ‚ C_e(14) [i] based on
  1. linear OA(9⁹⁹, 4782969, F₉, 16) (dual of [4782969, 4782870, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
  2. linear OA(9⁹², 4782969, F₉, 15) (dual of [4782969, 4782877, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
  3. linear OA(9⁰, 7, F₉, 0) (dual of [7, 7, 1]-code), using
    - discarding factors / shortening the dual code based on linear OA(9⁰, s, F₉, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
      - OA with only one run / dual of code without redundancy [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(3¹⁹⁸, 3188650, F₃, 3, 16) (dual of [(3188650, 3), 9565752, 17]-NRT-code)	[i]	Trace Code for OOAs
2	Linear OOA(9¹⁰⁸, 1594341, F₉, 3, 16) (dual of [(1594341, 3), 4782915, 17]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Linear OOA(9¹⁰⁹, 1594345, F₉, 3, 16) (dual of [(1594345, 3), 4782926, 17]-NRT-code)	[i]
4	Linear OOA(9¹¹⁰, 1594353, F₉, 3, 16) (dual of [(1594353, 3), 4782949, 17]-NRT-code)	[i]
5	Linear OOA(9¹¹¹, 1594355, F₉, 3, 16) (dual of [(1594355, 3), 4782954, 17]-NRT-code)	[i]
6	Linear OOA(9¹¹², 1594357, F₉, 3, 16) (dual of [(1594357, 3), 4782959, 17]-NRT-code)	[i]