MinT - Information on Result #1524820

Information on Result #1524820

Linear OOA(3¹⁵⁸, 8098, F₃, 3, 26) (dual of [(8098, 3), 24136, 27]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁵⁸, 8098, F₃, 2, 26) (dual of [(8098, 2), 16038, 27]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁵⁸, 9852, F₃, 2, 26) (dual of [(9852, 2), 19546, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹⁵⁸, 19704, F₃, 26) (dual of [19704, 19546, 27]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁵⁸, 19705, F₃, 26) (dual of [19705, 19547, 27]-code), using
    - constructionÂ X applied to C_e(25) âŠ‚ C_e(22) [i] based on
      1. linear OA(3¹⁵⁴, 19683, F₃, 26) (dual of [19683, 19529, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
      2. linear OA(3¹³⁶, 19683, F₃, 23) (dual of [19683, 19547, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
      3. linear OA(3⁴, 22, F₃, 2) (dual of [22, 18, 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(3¹⁵⁸, 4049, F₃, 5, 26) (dual of [(4049, 5), 20087, 27]-NRT-code)	[i]		OOA Folding