MinT - Information on Result #896161

Information on Result #896161

Linear OOA(5¹¹⁵, 4194365, F₅, 2, 13) (dual of [(4194365, 2), 8388615, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(5¹⁴, 64, F₅, 2, 6) (dual of [(64, 2), 114, 7]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5¹⁴, 128, F₅, 6) (dual of [128, 114, 7]-code), using
  - discarding factors / shortening the dual code based on linear OA(5¹⁴, 129, F₅, 6) (dual of [129, 115, 7]-code), using
    - constructionÂ X applied to C_e(5) âŠ‚ C_e(3) [i] based on
      1. 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]
      2. linear OA(5¹⁰, 125, F₅, 4) (dual of [125, 115, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 124Â = 5³âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
      3. linear OA(5¹, 4, F₅, 1) (dual of [4, 3, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(5¹, s, F₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
linear OOA(5¹⁰¹, 4194301, F₅, 2, 13) (dual of [(4194301, 2), 8388501, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5¹⁰¹, 8388602, F₅, 13) (dual of [8388602, 8388501, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(5¹⁰¹, large, F₅, 13) (dual of [large, large−101, 14]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 9765626Â | 5²⁰âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [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.