MinT - Information on Result #2641453

Information on Result #2641453

Linear OOA(5¹⁴⁰, large, F₅, 3, 9), using strength reduction based on linear OOA(5¹⁴⁰, large, F₅, 3, 11), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(5², 6, F₅, 3, 2) (dual of [(6, 3), 16, 3]-NRT-code), using
  - extended Reedâ€“Solomon NRT-code RS_e(3;16,5) [i]
2. linear OOA(5², 6, F₅, 3, 2) (dual of [(6, 3), 16, 3]-NRT-code) (see above)
3. linear OOA(5¹⁵, 2796201, F₅, 3, 3) (dual of [(2796201, 3), 8388588, 4]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(5¹⁵, 3050325, F₅, 3, 3) (dual of [(3050325, 3), 9150960, 4]-NRT-code), using
    - OOA stacking with additional row [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]
4. linear OOA(5⁴⁰, 2796201, F₅, 3, 5) (dual of [(2796201, 3), 8388563, 6]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(5⁴⁰, 4194301, F₅, 3, 5) (dual of [(4194301, 3), 12582863, 6]-NRT-code), using
    - OOA 2-folding and stacking with additional row [i] based on linear OA(5⁴⁰, large, F₅, 5) (dual of [large, large−40, 6]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 9765624Â = 5¹⁰âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
5. linear OOA(5⁸¹, 2796201, F₅, 3, 11) (dual of [(2796201, 3), 8388522, 12]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(5⁸¹, large, F₅, 11) (dual of [large, large−81, 12]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 9765626Â | 5²⁰âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and t, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(5¹⁴¹, large, F₅, 3, 9)	[i]		OOA Duplication
2	Linear OOA(5¹⁴², large, F₅, 3, 9)	[i]		OOA Duplication