MinT - Information on Result #1016076

Information on Result #1016076

Linear OOA(9⁵⁹, 19704, F₉, 3, 12) (dual of [(19704, 3), 59053, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(9⁸, 20, F₉, 3, 6) (dual of [(20, 3), 52, 7]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,53P) [i] based on function field F/F₉ with g(F) = 2 and N(F) ≥ 20, using
  - a function field by GarcÃa and Quoos [i]
linear OOA(9⁵¹, 19684, F₉, 3, 12) (dual of [(19684, 3), 59001, 13]-NRT-code), using
- OOA 3-folding [i] based on linear OA(9⁵¹, 59052, F₉, 12) (dual of [59052, 59001, 13]-code), using
  - discarding factors / shortening the dual code based on linear OA(9⁵¹, 59054, F₉, 12) (dual of [59054, 59003, 13]-code), using
    - constructionÂ X applied to C_e(11) âŠ‚ C_e(10) [i] based on
      1. linear OA(9⁵¹, 59049, F₉, 12) (dual of [59049, 58998, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 9⁵âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
      2. linear OA(9⁴⁶, 59049, F₉, 11) (dual of [59049, 59003, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 9⁵âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
      3. linear OA(9⁰, 5, F₉, 0) (dual of [5, 5, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(9⁰, s, F₉, 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(9⁵⁹, 9851, F₉, 15, 12) (dual of [(9851, 15), 147706, 13]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row