MinT - Information on Result #1520976

Information on Result #1520976

Linear OOA(3⁷¹, 24531, F₃, 3, 11) (dual of [(24531, 3), 73522, 12]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3⁷¹, 24531, F₃, 2, 11) (dual of [(24531, 2), 48991, 12]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3⁷¹, 29529, F₃, 2, 11) (dual of [(29529, 2), 58987, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3⁷¹, 59058, F₃, 11) (dual of [59058, 58987, 12]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁷¹, 59059, F₃, 11) (dual of [59059, 58988, 12]-code), using
    - constructionÂ X applied to C_e(10) âŠ‚ C_e(9) [i] based on
      1. linear OA(3⁷¹, 59049, F₃, 11) (dual of [59049, 58978, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
      2. linear OA(3⁶¹, 59049, F₃, 10) (dual of [59049, 58988, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
      3. linear OA(3⁰, 10, F₃, 0) (dual of [10, 10, 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(3⁷¹, 12265, F₃, 5, 11) (dual of [(12265, 5), 61254, 12]-NRT-code)	[i]		OOA Folding