MinT - Information on Result #735744

Information on Result #735744

Linear OA(128³⁹, 16515, F₁₂₈, 16) (dual of [16515, 16476, 17]-code), using (u,Â u+v)-construction based on

linear OA(128⁸, 129, F₁₂₈, 8) (dual of [129, 121, 9]-code or 129-arc in PG(7,128)), using
- extended Reedâ€“Solomon code RS_e(121,128) [i]
linear OA(128³¹, 16386, F₁₂₈, 16) (dual of [16386, 16355, 17]-code), using
- constructionÂ X applied to C_e(15) âŠ‚ C_e(14) [i] based on
  1. linear OA(128³¹, 16384, F₁₂₈, 16) (dual of [16384, 16353, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
  2. linear OA(128²⁹, 16384, F₁₂₈, 15) (dual of [16384, 16355, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
  3. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code), using
    - discarding factors / shortening the dual code based on linear OA(128⁰, s, F₁₂₈, 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		Method
1	Linear OOA(128³⁹, 16515, F₁₂₈, 2, 16) (dual of [(16515, 2), 32991, 17]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(128³⁹, 16515, F₁₂₈, 3, 16) (dual of [(16515, 3), 49506, 17]-NRT-code)	[i]
3	Linear OOA(128³⁹, 16515, F₁₂₈, 4, 16) (dual of [(16515, 4), 66021, 17]-NRT-code)	[i]
4	Digital (23, 39, 16515)-net over F₁₂₈	[i]
5	Linear OOA(128³⁹, 8257, F₁₂₈, 2, 16) (dual of [(8257, 2), 16475, 17]-NRT-code)	[i]	OOA Folding
6	Linear OOA(128³⁹, 5505, F₁₂₈, 3, 16) (dual of [(5505, 3), 16476, 17]-NRT-code)	[i]	OOA Folding