MinT - Information on Result #904268

Information on Result #904268

Linear OOA(81²⁰, 3381, F₈₁, 2, 8) (dual of [(3381, 2), 6742, 9]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(81⁵, 100, F₈₁, 2, 4) (dual of [(100, 2), 195, 5]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,195P) [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
  - a function field by SÃ©mirat [i]
linear OOA(81¹⁵, 3281, F₈₁, 2, 8) (dual of [(3281, 2), 6547, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(81¹⁵, 6562, F₈₁, 8) (dual of [6562, 6547, 9]-code), using
  - discarding factors / shortening the dual code based on linear OA(81¹⁵, 6563, F₈₁, 8) (dual of [6563, 6548, 9]-code), using
    - constructionÂ X applied to C_e(7) âŠ‚ C_e(6) [i] based on
      1. linear OA(81¹⁵, 6561, F₈₁, 8) (dual of [6561, 6546, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
      2. linear OA(81¹³, 6561, F₈₁, 7) (dual of [6561, 6548, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [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(81⁸¹, 4197682, F₈₁, 2, 16) (dual of [(4197682, 2), 8395283, 17]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs