MinT - Information on Result #1010839

Information on Result #1010839

Linear OOA(3²²², 4390528, F₃, 3, 16) (dual of [(4390528, 3), 13171362, 17]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁷¹, 1594327, F₃, 3, 8) (dual of [(1594327, 3), 4782910, 9]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3⁷¹, 4782981, F₃, 8) (dual of [4782981, 4782910, 9]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁷¹, 4782983, F₃, 8) (dual of [4782983, 4782912, 9]-code), using
    - constructionÂ X applied to C_e(7) âŠ‚ C_e(6) [i] based on
      1. linear OA(3⁷¹, 4782969, F₃, 8) (dual of [4782969, 4782898, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
      2. linear OA(3⁵⁷, 4782969, F₃, 7) (dual of [4782969, 4782912, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
      3. linear OA(3⁰, 14, F₃, 0) (dual of [14, 14, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]
linear OOA(3¹⁵¹, 2796201, F₃, 3, 16) (dual of [(2796201, 3), 8388452, 17]-NRT-code), using
- OOA 3-folding [i] 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: Constructive and 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

None.