MinT - Information on Result #2437037

Information on Result #2437037

Linear OOA(3²³², 88601, F₃, 2, 30) (dual of [(88601, 2), 176970, 31]-NRT-code), using strength reduction based on linear OOA(3²³², 88601, F₃, 2, 31) (dual of [(88601, 2), 176970, 32]-NRT-code), using

OOA 2-folding [i] based on linear OA(3²³², 177202, F₃, 31) (dual of [177202, 176970, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(3²³², 177203, F₃, 31) (dual of [177203, 176971, 32]-code), using
  - constructionÂ X applied to C([0,15]) âŠ‚ C([0,12]) [i] based on
    1. linear OA(3²²¹, 177148, F₃, 31) (dual of [177148, 176927, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 177148Â | 3²²âˆ’1, defining interval IÂ =Â [0,15], and minimum distance dÂ â‰¥ |{−15,−14,…,15}|+1Â =Â 32 (BCH-bound) [i]
    2. linear OA(3¹⁷⁷, 177148, F₃, 25) (dual of [177148, 176971, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 177148Â | 3²²âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
    3. linear OA(3¹¹, 55, F₃, 5) (dual of [55, 44, 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: Constructive and 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		Method
1	Linear OOA(3²³², 63323, F₃, 3, 30) (dual of [(63323, 3), 189737, 31]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3²³², 63323, F₃, 4, 30) (dual of [(63323, 4), 253060, 31]-NRT-code)	[i]
3	Linear OOA(3²³², 63323, F₃, 5, 30) (dual of [(63323, 5), 316383, 31]-NRT-code)	[i]
4	Digital (202, 232, 63323)-net over F₃	[i]