MinT - Information on Result #894863

Information on Result #894863

Linear OOA(3³⁹, 265730, F₃, 2, 5) (dual of [(265730, 2), 531421, 6]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3², 4, F₃, 2, 2) (dual of [(4, 2), 6, 3]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;6,3) [i]
linear OOA(3³⁷, 265726, F₃, 2, 5) (dual of [(265726, 2), 531415, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3³⁷, 531452, F₃, 5) (dual of [531452, 531415, 6]-code), using
  - discarding factors / shortening the dual code based on linear OA(3³⁷, 531453, F₃, 5) (dual of [531453, 531416, 6]-code), using
    - constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
      1. linear OA(3³⁷, 531441, F₃, 5) (dual of [531441, 531404, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
      2. linear OA(3²⁵, 531441, F₃, 4) (dual of [531441, 531416, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
      3. linear OA(3⁰, 12, F₃, 0) (dual of [12, 12, 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		Method
1	Linear OOA(3³⁹, 265729, F₃, 3, 5) (dual of [(265729, 3), 797148, 6]-NRT-code)	[i]	OOA Stacking with Additional Row
2	Linear OOA(3³⁹, 265729, F₃, 4, 5) (dual of [(265729, 4), 1062877, 6]-NRT-code)	[i]
3	Linear OOA(3³⁹, 265729, F₃, 5, 5) (dual of [(265729, 5), 1328606, 6]-NRT-code)	[i]