MinT - Information on Result #1648967

Information on Result #1648967

Linear OOA(3²¹⁰, 25855, F₃, 5, 30) (dual of [(25855, 5), 129065, 31]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²¹⁰, 25855, F₃, 2, 30) (dual of [(25855, 2), 51500, 31]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²¹⁰, 29549, F₃, 2, 30) (dual of [(29549, 2), 58888, 31]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3²¹⁰, 59098, F₃, 30) (dual of [59098, 58888, 31]-code), using
  - discarding factors / shortening the dual code based on linear OA(3²¹⁰, 59099, F₃, 30) (dual of [59099, 58889, 31]-code), using
    - constructionÂ X applied to C([0,15]) âŠ‚ C([0,12]) [i] based on
      1. linear OA(3²⁰¹, 59050, F₃, 31) (dual of [59050, 58849, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050Â | 3²⁰âˆ’1, defining interval IÂ =Â [0,15], and minimum distance dÂ â‰¥ |{−15,−14,…,15}|+1Â =Â 32 (BCH-bound) [i]
      2. linear OA(3¹⁶¹, 59050, F₃, 25) (dual of [59050, 58889, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050Â | 3²⁰âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
      3. linear OA(3⁹, 49, F₃, 4) (dual of [49, 40, 5]-code), using
        discarding factors / shortening the dual code based on linear OA(3⁹, 80, F₃, 4) (dual of [80, 71, 5]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 80Â = 3⁴âˆ’1, defining interval IÂ =Â [0,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [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, 8618, F₃, 35, 30) (dual of [(8618, 35), 301420, 31]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row