MinT - Information on Result #1652087

Information on Result #1652087

Linear OOA(3²⁴⁴, 139551, F₃, 5, 30) (dual of [(139551, 5), 697511, 31]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²⁴⁴, 139551, F₃, 3, 30) (dual of [(139551, 3), 418409, 31]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²⁴⁴, 177156, F₃, 3, 30) (dual of [(177156, 3), 531224, 31]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3²⁴⁴, 531468, F₃, 30) (dual of [531468, 531224, 31]-code), using
  - 1 times truncation [i] based on linear OA(3²⁴⁵, 531469, F₃, 31) (dual of [531469, 531224, 32]-code), using
    - constructionÂ X applied to C_e(30) âŠ‚ C_e(27) [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(3²¹⁷, 531441, F₃, 28) (dual of [531441, 531224, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
      3. linear OA(3⁴, 28, F₃, 2) (dual of [28, 24, 3]-code), using
        discarding factors / shortening the dual code based on linear OA(3⁴, 40, F₃, 2) (dual of [40, 36, 3]-code), using
        Hamming code H(4,3) [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(3²⁴⁴, 46516, F₃, 35, 30) (dual of [(46516, 35), 1627816, 31]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row