MinT - Information on Result #1643976

Information on Result #1643976

Linear OOA(3¹³⁸, 3102, F₃, 5, 26) (dual of [(3102, 5), 15372, 27]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹³⁸, 3102, F₃, 2, 26) (dual of [(3102, 2), 6066, 27]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹³⁸, 3285, F₃, 2, 26) (dual of [(3285, 2), 6432, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹³⁸, 6570, F₃, 26) (dual of [6570, 6432, 27]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(3¹³⁷, 6569, F₃, 26) (dual of [6569, 6432, 27]-code), using
    - constructionÂ X applied to C_e(25) âŠ‚ C_e(24) [i] based on
      1. linear OA(3¹³⁷, 6561, F₃, 26) (dual of [6561, 6424, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
      2. linear OA(3¹²⁹, 6561, F₃, 25) (dual of [6561, 6432, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
      3. linear OA(3⁰, 8, F₃, 0) (dual of [8, 8, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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(3¹³⁸, 1033, F₃, 35, 26) (dual of [(1033, 35), 36017, 27]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row