MinT - Information on Result #2694776

Information on Result #2694776

Linear OOA(5¹⁴¹, large, F₅, 3, 10), using 3 times NRT-code embedding in larger space based on linear OOA(5¹³², 8388602, F₅, 3, 10) (dual of [(8388602, 3), 25165674, 11]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. 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]
2. linear OOA(5⁹², 4194301, F₅, 3, 10) (dual of [(4194301, 3), 12582811, 11]-NRT-code), using
  - OOA 2-folding [i] based on linear OOA(5⁹², 8388602, F₅, 2, 10) (dual of [(8388602, 2), 16777112, 11]-NRT-code), using
    - trace code [i] based on linear OOA(25⁴⁶, 4194301, F₂₅, 2, 10) (dual of [(4194301, 2), 8388556, 11]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(25⁴⁶, 8388602, F₂₅, 10) (dual of [8388602, 8388556, 11]-code), using
        discarding factors / shortening the dual code based on linear OA(25⁴⁶, large, F₂₅, 10) (dual of [large, large−46, 11]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 25⁵âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [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(5¹⁴², large, F₅, 3, 10)	[i]		OOA Duplication
2	Linear OOA(5¹⁴³, large, F₅, 3, 10)	[i]		OOA Duplication