MinT - Information on Result #1604886

Information on Result #1604886

Linear OOA(3¹⁴⁶, 1282397, F₃, 4, 16) (dual of [(1282397, 4), 5129442, 17]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁴⁶, 1282397, F₃, 3, 16) (dual of [(1282397, 3), 3847045, 17]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁴⁶, 1594334, F₃, 3, 16) (dual of [(1594334, 3), 4782856, 17]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3¹⁴⁶, 4783002, F₃, 16) (dual of [4783002, 4782856, 17]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(3¹⁴⁵, 4783001, F₃, 16) (dual of [4783001, 4782856, 17]-code), using
    - constructionÂ X applied to C_e(15) âŠ‚ C_e(12) [i] based on
      1. linear OA(3¹⁴¹, 4782969, F₃, 16) (dual of [4782969, 4782828, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
      2. linear OA(3¹¹³, 4782969, F₃, 13) (dual of [4782969, 4782856, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      3. linear OA(3⁴, 32, F₃, 2) (dual of [32, 28, 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(3¹⁴⁶, 641198, F₃, 20, 16) (dual of [(641198, 20), 12823814, 17]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row