MinT - Information on Result #1832452

Information on Result #1832452

OOA(128⁵⁷, 4194687, S₁₂₈, 2, 14), using (u,Â u+v)-construction based on

OOA(128¹¹, 386, S₁₂₈, 2, 7), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(128³, 129, F₁₂₈, 2, 3) (dual of [(129, 2), 255, 4]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;255,128) [i]
  2. OOA(128⁸, 257, S₁₂₈, 2, 7), using
    - extracting embedded OOA [i] based on (1, 8, 257)-net in base 128, using
      - base change [i] based on digital (0, 7, 257)-net over F₂₅₆, using
        net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
        the rational function field F₂₅₆(x) [i]
        Niederreiter sequence [i]
OOA(128⁴⁶, 4194301, S₁₂₈, 2, 14), using
- OOA 2-folding [i] based on OA(128⁴⁶, 8388602, S₁₂₈, 14), using
  - discarding factors based on OA(128⁴⁶, large, S₁₂₈, 14), using
    - discarding parts of the base [i] based on linear OA(256⁴⁰, large, F₂₅₆, 14) (dual of [large, large−40, 15]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]

None.

The following results depend on this result:

	Result		This result only	Method
1	OOA(128⁵⁷, 2097343, S₁₂₈, 4, 14)	[i]		OOA Folding