MinT - Information on Result #904243

Information on Result #904243

Linear OOA(81¹⁴, 3363, F₈₁, 2, 6) (dual of [(3363, 2), 6712, 7]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(81³, 82, F₈₁, 2, 3) (dual of [(82, 2), 161, 4]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;161,81) [i]
linear OOA(81¹¹, 3281, F₈₁, 2, 6) (dual of [(3281, 2), 6551, 7]-NRT-code), using
- OOA 2-folding [i] based on linear OA(81¹¹, 6562, F₈₁, 6) (dual of [6562, 6551, 7]-code), using
  - discarding factors / shortening the dual code based on linear OA(81¹¹, 6563, F₈₁, 6) (dual of [6563, 6552, 7]-code), using
    - constructionÂ X applied to C_e(5) âŠ‚ C_e(4) [i] based on
      1. linear OA(81¹¹, 6561, F₈₁, 6) (dual of [6561, 6550, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
      2. linear OA(81⁹, 6561, F₈₁, 5) (dual of [6561, 6552, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
      3. linear OA(81⁰, 2, F₈₁, 0) (dual of [2, 2, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(81⁰, s, F₈₁, 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(81⁵⁹, 4197664, F₈₁, 2, 12) (dual of [(4197664, 2), 8395269, 13]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(81⁶³, 4197664, F₈₁, 2, 13) (dual of [(4197664, 2), 8395265, 14]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs