MinT - Information on Result #2487605

Information on Result #2487605

Linear OOA(3²⁵⁰, 88610, F₃, 2, 32) (dual of [(88610, 2), 176970, 33]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(3²⁴⁸, 88609, F₃, 2, 32) (dual of [(88609, 2), 176970, 33]-NRT-code), using

OOA 2-folding [i] based on linear OA(3²⁴⁸, 177218, F₃, 32) (dual of [177218, 176970, 33]-code), using
- constructionÂ X applied to C_e(31) âŠ‚ C_e(24) [i] based on
  1. linear OA(3²³², 177147, F₃, 32) (dual of [177147, 176915, 33]-code), using an extension C_e(31) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,31], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 32 [i]
  2. linear OA(3¹⁷⁷, 177147, F₃, 25) (dual of [177147, 176970, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
  3. linear OA(3¹⁶, 71, F₃, 6) (dual of [71, 55, 7]-code), using
    - discarding factors / shortening the dual code based on linear OA(3¹⁶, 80, F₃, 6) (dual of [80, 64, 7]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 80Â = 3⁴âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [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, 70166, F₃, 3, 32) (dual of [(70166, 3), 210248, 33]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3²⁵⁰, 70166, F₃, 4, 32) (dual of [(70166, 4), 280414, 33]-NRT-code)	[i]
3	Linear OOA(3²⁵⁰, 70166, F₃, 5, 32) (dual of [(70166, 5), 350580, 33]-NRT-code)	[i]
4	Digital (218, 250, 70166)-net over F₃	[i]