MinT - Information on Result #2694663

Information on Result #2694663

Linear OOA(5¹¹⁴, large, F₅, 3, 8), using 5² times duplication based on linear OOA(5¹¹², large, F₅, 3, 8), using

3 times NRT-code embedding in larger space [i] based on linear OOA(5¹⁰³, large, F₅, 3, 8), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(5¹¹, 2796201, F₅, 3, 2) (dual of [(2796201, 3), 8388592, 3]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(5¹¹, large, F₅, 3, 2), using
      - appending 1 arbitrary column [i] based on linear OOA(5¹¹, large, F₅, 2, 2), using
        appending kth column [i] based on linear OA(5¹¹, large, F₅, 2) (dual of [large, large−11, 3]-code), using
        Hamming code H(11,5) [i]
  2. linear OOA(5³¹, 2796201, F₅, 3, 4) (dual of [(2796201, 3), 8388572, 5]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(5³¹, 4194301, F₅, 3, 4) (dual of [(4194301, 3), 12582872, 5]-NRT-code), using
      - OA 2-folding and stacking [i] based on linear OA(5³¹, 8388602, F₅, 4) (dual of [8388602, 8388571, 5]-code), using
        discarding factors / shortening the dual code based on linear OA(5³¹, large, F₅, 4) (dual of [large, large−31, 5]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 5¹⁰âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
  3. linear OOA(5⁶¹, 2796201, F₅, 3, 8) (dual of [(2796201, 3), 8388542, 9]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(5⁶¹, large, F₅, 8) (dual of [large, large−61, 9]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 5¹⁰âˆ’1, defining interval IÂ =Â [0,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [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

None.