MinT - Information on Result #1645707

Information on Result #1645707

Linear OOA(3¹⁶⁷, 568931, F₃, 5, 18) (dual of [(568931, 5), 2844488, 19]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁶⁷, 568931, F₃, 2, 18) (dual of [(568931, 2), 1137695, 19]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁶⁷, 797193, F₃, 2, 18) (dual of [(797193, 2), 1594219, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹⁶⁷, 1594386, F₃, 18) (dual of [1594386, 1594219, 19]-code), using
  - 1 times truncation [i] based on linear OA(3¹⁶⁸, 1594387, F₃, 19) (dual of [1594387, 1594219, 20]-code), using
    - constructionÂ X applied to C([0,9]) âŠ‚ C([0,6]) [i] based on
      1. linear OA(3¹⁵⁷, 1594324, F₃, 19) (dual of [1594324, 1594167, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324Â | 3²⁶âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
      2. linear OA(3¹⁰⁵, 1594324, F₃, 13) (dual of [1594324, 1594219, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324Â | 3²⁶âˆ’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, 63, F₃, 5) (dual of [63, 52, 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(3¹⁶⁷, 284465, F₃, 25, 18) (dual of [(284465, 25), 7111458, 19]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row