MinT - Information on Result #1200337

Information on Result #1200337

Linear OOA(49³³, 3843207, F₄₉, 9, 7) (dual of [(3843207, 9), 34588830, 8]-NRT-code), using OOA stacking with additional row based on linear OOA(49³³, 3843208, F₄₉, 3, 7) (dual of [(3843208, 3), 11529591, 8]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(49⁷, 5769603, F₄₉, 3, 3) (dual of [(5769603, 3), 17308802, 4]-NRT-code), using
  - appending kth column [i] based on linear OOA(49⁷, 5769603, F₄₉, 2, 3) (dual of [(5769603, 2), 11539199, 4]-NRT-code), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(49⁷, 5769603, F₄₉, 3) (dual of [5769603, 5769596, 4]-code or 5769603-cap in PG(6,49)), using
      - product of two caps with tangent hyperplane [i]
2. linear OOA(49²⁶, 1921604, F₄₉, 3, 7) (dual of [(1921604, 3), 5764786, 8]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(49²⁶, 5764812, F₄₉, 7) (dual of [5764812, 5764786, 8]-code), using
    - constructionÂ X4 applied to C([0,3]) âŠ‚ C([0,2]) [i] based on
      1. linear OA(49²⁵, 5764802, F₄₉, 7) (dual of [5764802, 5764777, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 5764802Â | 49⁸âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
      2. linear OA(49¹⁷, 5764802, F₄₉, 5) (dual of [5764802, 5764785, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 5764802Â | 49⁸âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
      3. linear OA(49⁹, 10, F₄₉, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,49)), using
        dual of repetition code with length 10 [i]
      4. linear OA(49¹, 10, F₄₉, 1) (dual of [10, 9, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(49¹, 49, F₄₉, 1) (dual of [49, 48, 2]-code), using
        Reedâ€“Solomon code RS(48,49) [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 (26, 33, 3843207)-net over F₄₉	[i]		Net Defined by OOA