MinT - Information on Result #1652684

Information on Result #1652684

Linear OOA(3²⁵⁰, 132871, F₃, 5, 31) (dual of [(132871, 5), 664105, 32]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²⁵⁰, 132871, F₃, 4, 31) (dual of [(132871, 4), 531234, 32]-NRT-code), using

OOA 4-folding [i] based on linear OA(3²⁵⁰, 531484, F₃, 31) (dual of [531484, 531234, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(3²⁵⁰, 531486, F₃, 31) (dual of [531486, 531236, 32]-code), using
  - constructionÂ X applied to C_e(30) âŠ‚ C_e(25) [i] based on
    1. linear OA(3²⁴¹, 531441, F₃, 31) (dual of [531441, 531200, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
    2. linear OA(3²⁰⁵, 531441, F₃, 26) (dual of [531441, 531236, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
    3. linear OA(3⁹, 45, F₃, 4) (dual of [45, 36, 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(3²⁵⁰, 44290, F₃, 35, 31) (dual of [(44290, 35), 1549900, 32]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row