MinT - Information on Result #1642922

Information on Result #1642922

Linear OOA(3¹¹⁷, 3291, F₃, 5, 21) (dual of [(3291, 5), 16338, 22]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹¹⁷, 3291, F₃, 2, 21) (dual of [(3291, 2), 6465, 22]-NRT-code), using

1 times NRT-code embedding in larger space [i] based on linear OOA(3¹¹⁵, 3290, F₃, 2, 21) (dual of [(3290, 2), 6465, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹¹⁵, 6580, F₃, 21) (dual of [6580, 6465, 22]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(3¹¹⁴, 6579, F₃, 21) (dual of [6579, 6465, 22]-code), using
    - constructionÂ X applied to C([0,10]) âŠ‚ C([0,9]) [i] based on
      1. linear OA(3¹¹³, 6562, F₃, 21) (dual of [6562, 6449, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562Â | 3¹⁶âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
      2. linear OA(3⁹⁷, 6562, F₃, 19) (dual of [6562, 6465, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562Â | 3¹⁶âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
      3. linear OA(3¹, 17, F₃, 1) (dual of [17, 16, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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(3¹¹⁷, 1645, F₃, 25, 21) (dual of [(1645, 25), 41008, 22]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row