MinT - Information on Result #1602314

Information on Result #1602314

Linear OOA(3⁹⁰, 3003, F₃, 4, 17) (dual of [(3003, 4), 11922, 18]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3⁹⁰, 3003, F₃, 2, 17) (dual of [(3003, 2), 5916, 18]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3⁹⁰, 3285, F₃, 2, 17) (dual of [(3285, 2), 6480, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3⁹⁰, 6570, F₃, 17) (dual of [6570, 6480, 18]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(3⁸⁹, 6569, F₃, 17) (dual of [6569, 6480, 18]-code), using
    - constructionÂ X applied to C_e(16) âŠ‚ C_e(15) [i] based on
      1. linear OA(3⁸⁹, 6561, F₃, 17) (dual of [6561, 6472, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
      2. linear OA(3⁸¹, 6561, F₃, 16) (dual of [6561, 6480, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
      3. linear OA(3⁰, 8, F₃, 0) (dual of [8, 8, 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]

Mode: 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		This result only	Method
1	Linear OOA(3⁹⁰, 1501, F₃, 20, 17) (dual of [(1501, 20), 29930, 18]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row