MinT - Information on Result #1013767

Information on Result #1013767

Linear OOA(7⁵⁶, 274537, F₇, 3, 9) (dual of [(274537, 3), 823555, 10]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(7⁶, 21, F₇, 3, 4) (dual of [(21, 3), 57, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(7⁶, 42, F₇, 4) (dual of [42, 36, 5]-code), using
  - 1 times truncation [i] based on linear OA(7⁷, 43, F₇, 5) (dual of [43, 36, 6]-code), using
    - a code by Danev and Olsson [i]
linear OOA(7⁵⁰, 274516, F₇, 3, 9) (dual of [(274516, 3), 823498, 10]-NRT-code), using
- OOA 3-folding [i] based on linear OA(7⁵⁰, 823548, F₇, 9) (dual of [823548, 823498, 10]-code), using
  - discarding factors / shortening the dual code based on linear OA(7⁵⁰, 823550, F₇, 9) (dual of [823550, 823500, 10]-code), using
    - constructionÂ X applied to C_e(8) âŠ‚ C_e(7) [i] based on
      1. linear OA(7⁵⁰, 823543, F₇, 9) (dual of [823543, 823493, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 823542Â = 7⁷âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
      2. linear OA(7⁴³, 823543, F₇, 8) (dual of [823543, 823500, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 823542Â = 7⁷âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
      3. linear OA(7⁰, 7, F₇, 0) (dual of [7, 7, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(7⁰, s, F₇, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

Mode: Constructive and linear.

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

None.