MinT - Information on Result #896232

Information on Result #896232

Linear OOA(5¹⁴⁶, 4194327, F₅, 2, 17) (dual of [(4194327, 2), 8388508, 18]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(5¹⁵, 26, F₅, 2, 8) (dual of [(26, 2), 37, 9]-NRT-code), using
- extracting embedded OOA [i] based on digital (7, 15, 26)-net over F₅, using
  - base reduction for projective spaces (embedding PG(7,25) in PG(14,5)) 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(5¹³¹, 4194301, F₅, 2, 17) (dual of [(4194301, 2), 8388471, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5¹³¹, 8388602, F₅, 17) (dual of [8388602, 8388471, 18]-code), using
  - discarding factors / shortening the dual code based on linear OA(5¹³¹, large, F₅, 17) (dual of [large, large−131, 18]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 5¹⁰âˆ’1, defining interval IÂ =Â [0,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(5¹⁴⁶, 1048581, F₅, 18, 17) (dual of [(1048581, 18), 18874312, 18]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row