MinT - Information on Result #897425

Information on Result #897425

Linear OOA(9⁴⁹, 531460, F₉, 2, 8) (dual of [(531460, 2), 1062871, 9]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(9⁵, 16, F₉, 2, 4) (dual of [(16, 2), 27, 5]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,27P) [i] based on function field F/F₉ with g(F) = 1 and N(F) ≥ 16, using
  - a function field by GarcÃa and Quoos [i]
linear OOA(9⁴⁴, 531444, F₉, 2, 8) (dual of [(531444, 2), 1062844, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(9⁴⁴, 1062888, F₉, 8) (dual of [1062888, 1062844, 9]-code), using
  - trace code [i] based on linear OA(81²², 531444, F₈₁, 8) (dual of [531444, 531422, 9]-code), using
    - constructionÂ X applied to C_e(7) âŠ‚ C_e(6) [i] based on
      1. linear OA(81²², 531441, F₈₁, 8) (dual of [531441, 531419, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
      2. linear OA(81¹⁹, 531441, F₈₁, 7) (dual of [531441, 531422, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
      3. linear OA(81⁰, 3, F₈₁, 0) (dual of [3, 3, 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(9⁴⁹, 265729, F₉, 10, 8) (dual of [(265729, 10), 2657241, 9]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row