MinT - Information on Result #1082511

Information on Result #1082511

Linear OOA(81⁶⁵, 2274298, F₈₁, 4, 13) (dual of [(2274298, 4), 9097127, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(81¹⁶, 177148, F₈₁, 4, 6) (dual of [(177148, 4), 708576, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(81¹⁶, 531444, F₈₁, 6) (dual of [531444, 531428, 7]-code), using
  - constructionÂ X applied to C_e(5) âŠ‚ C_e(4) [i] based on
    1. linear OA(81¹⁶, 531441, F₈₁, 6) (dual of [531441, 531425, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
    2. linear OA(81¹³, 531441, F₈₁, 5) (dual of [531441, 531428, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
    3. linear OA(81⁰, 3, F₈₁, 0) (dual of [3, 3, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(81⁰, s, F₈₁, 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(81⁴⁹, 2097150, F₈₁, 4, 13) (dual of [(2097150, 4), 8388551, 14]-NRT-code), using
- OOA 4-folding [i] based on linear OA(81⁴⁹, 8388600, F₈₁, 13) (dual of [8388600, 8388551, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(81⁴⁹, large, F₈₁, 13) (dual of [large, large−49, 14]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’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.