MinT - Information on Result #1080854

Information on Result #1080854

Linear OOA(3⁴⁰, 552, F₃, 4, 8) (dual of [(552, 4), 2168, 9]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁴, 4, F₃, 4, 4) (dual of [(4, 4), 12, 5]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(4;12,3) [i]
linear OOA(3³⁶, 548, F₃, 4, 8) (dual of [(548, 4), 2156, 9]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3³⁶, 2192, F₃, 8) (dual of [2192, 2156, 9]-code), using
  - discarding factors / shortening the dual code based on linear OA(3³⁶, 2194, F₃, 8) (dual of [2194, 2158, 9]-code), using
    - constructionÂ X applied to C_e(7) âŠ‚ C_e(6) [i] based on
      1. linear OA(3³⁶, 2187, F₃, 8) (dual of [2187, 2151, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 2186Â = 3⁷âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
      2. linear OA(3²⁹, 2187, F₃, 7) (dual of [2187, 2158, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 2186Â = 3⁷âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
      3. linear OA(3⁰, 7, F₃, 0) (dual of [7, 7, 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: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3¹⁹¹, 2097702, F₃, 4, 16) (dual of [(2097702, 4), 8390617, 17]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(3²⁰⁶, 2097702, F₃, 4, 17) (dual of [(2097702, 4), 8390602, 18]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs