MinT - Information on Result #1602483

Information on Result #1602483

Linear OOA(3⁹⁵, 7327, F₃, 4, 16) (dual of [(7327, 4), 29213, 17]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3⁹⁵, 7327, F₃, 2, 16) (dual of [(7327, 2), 14559, 17]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3⁹⁵, 9852, F₃, 2, 16) (dual of [(9852, 2), 19609, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3⁹⁵, 19704, F₃, 16) (dual of [19704, 19609, 17]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁹⁵, 19705, F₃, 16) (dual of [19705, 19610, 17]-code), using
    - constructionÂ X applied to C_e(15) âŠ‚ C_e(12) [i] based on
      1. linear OA(3⁹¹, 19683, F₃, 16) (dual of [19683, 19592, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
      2. linear OA(3⁷³, 19683, F₃, 13) (dual of [19683, 19610, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      3. linear OA(3⁴, 22, F₃, 2) (dual of [22, 18, 3]-code), using
        discarding factors / shortening the dual code based on linear OA(3⁴, 40, F₃, 2) (dual of [40, 36, 3]-code), using
        Hamming code H(4,3) [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(3⁹⁵, 3663, F₃, 20, 16) (dual of [(3663, 20), 73165, 17]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row