MinT - Information on Result #897606

Information on Result #897606

Linear OOA(9¹⁰⁴, 29555, F₉, 2, 21) (dual of [(29555, 2), 59006, 22]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(9¹³, 28, F₉, 2, 10) (dual of [(28, 2), 43, 11]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,45P) [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using
  - the Hermitian function field over F₉ [i]
linear OOA(9⁹¹, 29527, F₉, 2, 21) (dual of [(29527, 2), 58963, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(9⁹¹, 59054, F₉, 21) (dual of [59054, 58963, 22]-code), using
  - constructionÂ X applied to C_e(20) âŠ‚ C_e(19) [i] based on
    1. linear OA(9⁹¹, 59049, F₉, 21) (dual of [59049, 58958, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 9⁵âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
    2. linear OA(9⁸⁶, 59049, F₉, 20) (dual of [59049, 58963, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 9⁵âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [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(9¹⁰⁴, 5910, F₉, 22, 21) (dual of [(5910, 22), 129916, 22]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row