MinT - Information on Result #894861

Information on Result #894861

Linear OOA(3³³, 29533, F₃, 2, 5) (dual of [(29533, 2), 59033, 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(3³¹, 29529, F₃, 2, 5) (dual of [(29529, 2), 59027, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3³¹, 59058, F₃, 5) (dual of [59058, 59027, 6]-code), using
  - discarding factors / shortening the dual code based on linear OA(3³¹, 59059, F₃, 5) (dual of [59059, 59028, 6]-code), using
    - constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
      1. linear OA(3³¹, 59049, F₃, 5) (dual of [59049, 59018, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
      2. linear OA(3²¹, 59049, F₃, 4) (dual of [59049, 59028, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [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: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(3³³, 29532, F₃, 3, 5) (dual of [(29532, 3), 88563, 6]-NRT-code)	[i]	OOA Stacking with Additional Row
2	Linear OOA(3³³, 29532, F₃, 4, 5) (dual of [(29532, 4), 118095, 6]-NRT-code)	[i]
3	Linear OOA(3³³, 29532, F₃, 5, 5) (dual of [(29532, 5), 147627, 6]-NRT-code)	[i]