MinT - Information on Result #1016255

Information on Result #1016255

Linear OOA(9¹⁴⁴, 5596859, F₉, 3, 15) (dual of [(5596859, 3), 16790433, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(9³⁰, 4457, F₉, 3, 7) (dual of [(4457, 3), 13341, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(9⁴, 82, F₉, 3, 3) (dual of [(82, 3), 242, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(9⁴, 82, F₉, 2, 3) (dual of [(82, 2), 160, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(9⁴, 82, F₉, 3) (dual of [82, 78, 4]-code or 82-cap in PG(3,9)), using
        ovoid in PG(3,Â 9) [i]
  2. linear OOA(9²⁶, 4375, F₉, 3, 7) (dual of [(4375, 3), 13099, 8]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(9²⁶, 13125, F₉, 7) (dual of [13125, 13099, 8]-code), using
      - discarding factors / shortening the dual code based on linear OA(9²⁶, 13126, F₉, 7) (dual of [13126, 13100, 8]-code), using
        trace code [i] based on linear OA(81¹³, 6563, F₈₁, 7) (dual of [6563, 6550, 8]-code), using
        constructionÂ X applied to C_e(6) âŠ‚ C_e(5) [i] based on
        linear OA(81¹³, 6561, F₈₁, 7) (dual of [6561, 6548, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
        linear OA(81¹¹, 6561, F₈₁, 6) (dual of [6561, 6550, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
        linear OA(81⁰, 2, F₈₁, 0) (dual of [2, 2, 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(9¹¹⁴, 5592402, F₉, 3, 15) (dual of [(5592402, 3), 16777092, 16]-NRT-code), using
- trace code [i] based on linear OOA(81⁵⁷, 2796201, F₈₁, 3, 15) (dual of [(2796201, 3), 8388546, 16]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(81⁵⁷, large, F₈₁, 15) (dual of [large, large−57, 16]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (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.