MinT - Information on Result #1188165

Information on Result #1188165

Linear OOA(5⁵⁶, 5592401, F₅, 9, 6) (dual of [(5592401, 9), 50331553, 7]-NRT-code), using OOA stacking with additional row based on linear OOA(5⁵⁶, 5592402, F₅, 3, 6) (dual of [(5592402, 3), 16777150, 7]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(5¹⁵, 3050326, F₅, 3, 3) (dual of [(3050326, 3), 9150963, 4]-NRT-code), using
  - appending kth column [i] based on linear OOA(5¹⁵, 3050326, F₅, 2, 3) (dual of [(3050326, 2), 6100637, 4]-NRT-code), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(5¹⁵, 3050326, F₅, 3) (dual of [3050326, 3050311, 4]-code or 3050326-cap in PG(14,5)), using
      - product of projective cap with cap in AG(6,Â 5) [i] based on linear OA(5⁹, 4700, F₅, 3) (dual of [4700, 4691, 4]-code or 4700-cap in PG(8,5)), using
        caps completed using a computer search [i]
2. linear OOA(5⁴¹, 2796201, F₅, 3, 6) (dual of [(2796201, 3), 8388562, 7]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(5⁴¹, large, F₅, 6) (dual of [large, large−41, 7]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 5¹⁰âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]

Mode: Constructive and linear.

Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (50, 56, 5592401)-net over F₅	[i]		Net Defined by OOA