MinT - Information on Result #815791

Information on Result #815791

Linear OOA(3²⁵⁰, 29549, F₃, 2, 36) (dual of [(29549, 2), 58848, 37]-NRT-code), using OOA 2-folding based on linear OA(3²⁵⁰, 59098, F₃, 36) (dual of [59098, 58848, 37]-code), using

discarding factors / shortening the dual code based on linear OA(3²⁵⁰, 59099, F₃, 36) (dual of [59099, 58849, 37]-code), using
- constructionÂ X applied to C([0,18]) âŠ‚ C([0,15]) [i] based on
  1. linear OA(3²⁴¹, 59050, F₃, 37) (dual of [59050, 58809, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050Â | 3²⁰âˆ’1, defining interval IÂ =Â [0,18], and minimum distance dÂ â‰¥ |{−18,−17,…,18}|+1Â =Â 38 (BCH-bound) [i]
  2. 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]
  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: Constructive and 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		Method
1	Linear OOA(3²⁵⁰, 25317, F₃, 3, 36) (dual of [(25317, 3), 75701, 37]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3²⁵⁰, 25317, F₃, 4, 36) (dual of [(25317, 4), 101018, 37]-NRT-code)	[i]
3	Linear OOA(3²⁵⁰, 25317, F₃, 5, 36) (dual of [(25317, 5), 126335, 37]-NRT-code)	[i]
4	Digital (214, 250, 25317)-net over F₃	[i]