MinT - Information on Result #1648966

Information on Result #1648966

Linear OOA(3²¹⁰, 19757, F₃, 5, 31) (dual of [(19757, 5), 98575, 32]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²¹⁰, 19757, F₃, 2, 31) (dual of [(19757, 2), 39304, 32]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²¹⁰, 29544, F₃, 2, 31) (dual of [(29544, 2), 58878, 32]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3²¹⁰, 59088, F₃, 31) (dual of [59088, 58878, 32]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(3²⁰⁹, 59087, F₃, 31) (dual of [59087, 58878, 32]-code), using
    - constructionÂ X applied to C_e(30) âŠ‚ C_e(25) [i] based on
      1. linear OA(3²⁰¹, 59049, F₃, 31) (dual of [59049, 58848, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
      2. linear OA(3¹⁷¹, 59049, F₃, 26) (dual of [59049, 58878, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [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(3²¹⁰, 6585, F₃, 35, 31) (dual of [(6585, 35), 230265, 32]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row