MinT - Information on Result #735812

Information on Result #735812

Linear OA(128⁴⁰, 2097284, F₁₂₈, 12) (dual of [2097284, 2097244, 13]-code), using (u,Â u+v)-construction based on

linear OA(128⁶, 129, F₁₂₈, 6) (dual of [129, 123, 7]-code or 129-arc in PG(5,128)), using
- extended Reedâ€“Solomon code RS_e(123,128) [i]
linear OA(128³⁴, 2097155, F₁₂₈, 12) (dual of [2097155, 2097121, 13]-code), using
- constructionÂ X applied to C_e(11) âŠ‚ C_e(10) [i] based on
  1. linear OA(128³⁴, 2097152, F₁₂₈, 12) (dual of [2097152, 2097118, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
  2. linear OA(128³¹, 2097152, F₁₂₈, 11) (dual of [2097152, 2097121, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
  3. linear OA(128⁰, 3, F₁₂₈, 0) (dual of [3, 3, 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(128⁴⁰, 2097284, F₁₂₈, 2, 12) (dual of [(2097284, 2), 4194528, 13]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(128⁴⁰, 2097284, F₁₂₈, 3, 12) (dual of [(2097284, 3), 6291812, 13]-NRT-code)	[i]
3	Linear OOA(128⁴⁰, 2097284, F₁₂₈, 4, 12) (dual of [(2097284, 4), 8389096, 13]-NRT-code)	[i]
4	Digital (28, 40, 2097284)-net over F₁₂₈	[i]
5	Linear OOA(128⁴⁰, 1048642, F₁₂₈, 2, 12) (dual of [(1048642, 2), 2097244, 13]-NRT-code)	[i]	OOA Folding
6	Linear OOA(128⁴⁰, 699094, F₁₂₈, 3, 12) (dual of [(699094, 3), 2097242, 13]-NRT-code)	[i]	OOA Folding