MinT - Information on Result #1528898

Information on Result #1528898

Linear OOA(3²⁰⁸, 23832, F₃, 3, 30) (dual of [(23832, 3), 71288, 31]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²⁰⁸, 23832, F₃, 2, 30) (dual of [(23832, 2), 47456, 31]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²⁰⁸, 29543, F₃, 2, 30) (dual of [(29543, 2), 58878, 31]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3²⁰⁸, 59086, F₃, 30) (dual of [59086, 58878, 31]-code), using
  - 1 times truncation [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(3²⁰⁸, 11916, F₃, 5, 30) (dual of [(11916, 5), 59372, 31]-NRT-code)	[i]		OOA Folding