MinT - Information on Result #896212

Information on Result #896212

Linear OOA(5¹³⁷, 4194353, F₅, 2, 16) (dual of [(4194353, 2), 8388569, 17]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(5¹⁶, 52, F₅, 2, 8) (dual of [(52, 2), 88, 9]-NRT-code), using
- extracting embedded OOA [i] based on digital (8, 16, 52)-net over F₅, using
  - trace code for nets [i] based on digital (0, 8, 26)-net over F₂₅, using
    - net from sequence [i] based on digital (0, 25)-sequence over F₂₅, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26, using
        the rational function field F₂₅(x) [i]
      - Niederreiter sequence [i]
linear OOA(5¹²¹, 4194301, F₅, 2, 16) (dual of [(4194301, 2), 8388481, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5¹²¹, 8388602, F₅, 16) (dual of [8388602, 8388481, 17]-code), using
  - discarding factors / shortening the dual code based on linear OA(5¹²¹, large, F₅, 16) (dual of [large, large−121, 17]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 5¹⁰âˆ’1, defining interval IÂ =Â [0,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(5¹³⁸, 4194353, F₅, 2, 16) (dual of [(4194353, 2), 8388568, 17]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(5¹³⁷, 1048588, F₅, 18, 16) (dual of [(1048588, 18), 18874447, 17]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row