MinT - Information on Result #1651991

Information on Result #1651991

Linear OOA(3²⁴³, 1168287, F₃, 5, 26) (dual of [(1168287, 5), 5841192, 27]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²⁴³, 1168287, F₃, 4, 26) (dual of [(1168287, 4), 4672905, 27]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²⁴³, 1195750, F₃, 4, 26) (dual of [(1195750, 4), 4782757, 27]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3²⁴³, 4783000, F₃, 26) (dual of [4783000, 4782757, 27]-code), using
  - discarding factors / shortening the dual code based on linear OA(3²⁴³, 4783001, F₃, 26) (dual of [4783001, 4782758, 27]-code), using
    - constructionÂ X applied to C_e(25) âŠ‚ C_e(22) [i] based on
      1. linear OA(3²³⁹, 4782969, F₃, 26) (dual of [4782969, 4782730, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
      2. linear OA(3²¹¹, 4782969, F₃, 23) (dual of [4782969, 4782758, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 3¹⁴âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
      3. linear OA(3⁴, 32, F₃, 2) (dual of [32, 28, 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(3²⁴³, 389428, F₃, 35, 26) (dual of [(389428, 35), 13629737, 27]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row