MinT - Information on Result #1527857

Information on Result #1527857

Linear OOA(3¹⁹⁷, 26776, F₃, 3, 28) (dual of [(26776, 3), 80131, 29]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁹⁷, 26776, F₃, 2, 28) (dual of [(26776, 2), 53355, 29]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁹⁷, 29557, F₃, 2, 28) (dual of [(29557, 2), 58917, 29]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3¹⁹⁷, 59114, F₃, 28) (dual of [59114, 58917, 29]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁹⁷, 59115, F₃, 28) (dual of [59115, 58918, 29]-code), using
    - constructionÂ X applied to C_e(27) âŠ‚ C_e(19) [i] based on
      1. linear OA(3¹⁸¹, 59049, F₃, 28) (dual of [59049, 58868, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
      2. linear OA(3¹³¹, 59049, F₃, 20) (dual of [59049, 58918, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
      3. linear OA(3¹⁶, 66, F₃, 7) (dual of [66, 50, 8]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹⁶, 82, F₃, 7) (dual of [82, 66, 8]-code), using
        generator matrices provided on Edelâ€™s homepage [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(3¹⁹⁷, 13388, F₃, 5, 28) (dual of [(13388, 5), 66743, 29]-NRT-code)	[i]		OOA Folding