MinT - Information on Result #1644939

Information on Result #1644939

Linear OOA(3¹⁵⁵, 236237, F₃, 5, 18) (dual of [(236237, 5), 1181030, 19]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁵⁵, 236237, F₃, 2, 18) (dual of [(236237, 2), 472319, 19]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁵⁵, 265750, F₃, 2, 18) (dual of [(265750, 2), 531345, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹⁵⁵, 531500, F₃, 18) (dual of [531500, 531345, 19]-code), using
  - 1 times truncation [i] based on linear OA(3¹⁵⁶, 531501, F₃, 19) (dual of [531501, 531345, 20]-code), using
    - constructionÂ X applied to C([0,9]) âŠ‚ C([0,6]) [i] based on
      1. linear OA(3¹⁴⁵, 531442, F₃, 19) (dual of [531442, 531297, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442Â | 3²⁴âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
      2. linear OA(3⁹⁷, 531442, F₃, 13) (dual of [531442, 531345, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442Â | 3²⁴âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]
      3. linear OA(3¹¹, 59, F₃, 5) (dual of [59, 48, 6]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹¹, 85, F₃, 5) (dual of [85, 74, 6]-code), using
        codes constructed by inverting constructionÂ Y₁ [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(3¹⁵⁵, 118118, F₃, 25, 18) (dual of [(118118, 25), 2952795, 19]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row