MinT - Information on Result #896199

Information on Result #896199

Linear OOA(5¹³⁶, 4194365, F₅, 2, 15) (dual of [(4194365, 2), 8388594, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(5¹⁶, 64, F₅, 2, 7) (dual of [(64, 2), 112, 8]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5¹⁶, 128, F₅, 7) (dual of [128, 112, 8]-code), using
  - constructionÂ X applied to C_e(6) âŠ‚ C_e(5) [i] based on
    1. linear OA(5¹⁶, 125, F₅, 7) (dual of [125, 109, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 124Â = 5³âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
    2. linear OA(5¹³, 125, F₅, 6) (dual of [125, 112, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 124Â = 5³âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
    3. linear OA(5⁰, 3, F₅, 0) (dual of [3, 3, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(5⁰, s, F₅, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]
linear OOA(5¹²⁰, 4194301, F₅, 2, 15) (dual of [(4194301, 2), 8388482, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5¹²⁰, 8388602, F₅, 15) (dual of [8388602, 8388482, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(5¹²⁰, large, F₅, 15) (dual of [large, large−120, 16]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 9765624Â = 5¹⁰âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

Mode: Constructive and linear.

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

None.