MinT - Information on Result #1603626

Information on Result #1603626

Linear OOA(3¹²², 142479, F₃, 4, 16) (dual of [(142479, 4), 569794, 17]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹²², 142479, F₃, 3, 16) (dual of [(142479, 3), 427315, 17]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹²², 177151, F₃, 3, 16) (dual of [(177151, 3), 531331, 17]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3¹²², 531453, F₃, 16) (dual of [531453, 531331, 17]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹²², 531454, F₃, 16) (dual of [531454, 531332, 17]-code), using
    - constructionÂ X applied to C_e(15) âŠ‚ C_e(13) [i] based on
      1. linear OA(3¹²¹, 531441, F₃, 16) (dual of [531441, 531320, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
      2. linear OA(3¹⁰⁹, 531441, F₃, 14) (dual of [531441, 531332, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
      3. linear OA(3¹, 13, F₃, 1) (dual of [13, 12, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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(3¹²², 71239, F₃, 20, 16) (dual of [(71239, 20), 1424658, 17]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row