MinT - Information on Result #1522277

Information on Result #1522277

Linear OOA(3¹¹⁰, 26059, F₃, 3, 16) (dual of [(26059, 3), 78067, 17]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹¹⁰, 26059, F₃, 2, 16) (dual of [(26059, 2), 52008, 17]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹¹⁰, 29544, F₃, 2, 16) (dual of [(29544, 2), 58978, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹¹⁰, 59088, F₃, 16) (dual of [59088, 58978, 17]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(3¹⁰⁹, 59087, F₃, 16) (dual of [59087, 58978, 17]-code), using
    - constructionÂ X applied to C_e(15) âŠ‚ C_e(10) [i] based on
      1. linear OA(3¹⁰¹, 59049, F₃, 16) (dual of [59049, 58948, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
      2. linear OA(3⁷¹, 59049, F₃, 11) (dual of [59049, 58978, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
      3. linear OA(3⁸, 38, F₃, 4) (dual of [38, 30, 5]-code), using
        discarding factors / shortening the dual code based on linear OA(3⁸, 41, F₃, 4) (dual of [41, 33, 5]-code), using
        the narrow-sense BCH-code C(I) with length 41Â | 3⁸âˆ’1, defining interval IÂ =Â [1,1], and minimum distance dÂ â‰¥ |{−3,−1,1,3}|+1Â =Â 5 (BCH-bound) [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(3¹¹⁰, 13029, F₃, 5, 16) (dual of [(13029, 5), 65035, 17]-NRT-code)	[i]		OOA Folding