MinT - Information on Result #2699342

Information on Result #2699342

Linear OOA(8¹⁵¹, 6291458, F₈, 3, 14) (dual of [(6291458, 3), 18874223, 15]-NRT-code), using 8¹ times duplication based on linear OOA(8¹⁵⁰, 6291458, F₈, 3, 14) (dual of [(6291458, 3), 18874224, 15]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(8⁴⁴, 699056, F₈, 3, 7) (dual of [(699056, 3), 2097124, 8]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(8⁴⁴, 2097168, F₈, 7) (dual of [2097168, 2097124, 8]-code), using
    - constructionÂ X applied to C([0,3]) âŠ‚ C([0,2]) [i] based on
      1. linear OA(8⁴³, 2097153, F₈, 7) (dual of [2097153, 2097110, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153Â | 8¹⁴âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
      2. linear OA(8²⁹, 2097153, F₈, 5) (dual of [2097153, 2097124, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153Â | 8¹⁴âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
      3. linear OA(8¹, 15, F₈, 1) (dual of [15, 14, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(8¹, s, F₈, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
2. linear OOA(8¹⁰⁶, 5592402, F₈, 3, 14) (dual of [(5592402, 3), 16777100, 15]-NRT-code), using
  - trace code [i] based on linear OOA(64⁵³, 2796201, F₆₄, 3, 14) (dual of [(2796201, 3), 8388550, 15]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(64⁵³, large, F₆₄, 14) (dual of [large, large−53, 15]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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.