MinT - Information on Result #897526

Information on Result #897526

Linear OOA(9¹¹⁰, 2391516, F₉, 2, 16) (dual of [(2391516, 2), 4782922, 17]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(9¹¹, 28, F₉, 2, 8) (dual of [(28, 2), 45, 9]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,47P) [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(9⁹⁹, 2391488, F₉, 2, 16) (dual of [(2391488, 2), 4782877, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(9⁹⁹, 4782976, F₉, 16) (dual of [4782976, 4782877, 17]-code), using
  - constructionÂ X applied to C_e(15) âŠ‚ C_e(14) [i] based on
    1. linear OA(9⁹⁹, 4782969, F₉, 16) (dual of [4782969, 4782870, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
    2. linear OA(9⁹², 4782969, F₉, 15) (dual of [4782969, 4782877, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 4782968Â = 9⁷âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
    3. linear OA(9⁰, 7, F₉, 0) (dual of [7, 7, 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(9¹¹⁰, 597878, F₉, 18, 16) (dual of [(597878, 18), 10761694, 17]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row