MinT - Information on Result #1013789

Information on Result #1013789

Linear OOA(7¹⁰³, 7688756, F₇, 3, 9) (dual of [(7688756, 3), 23066165, 10]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(7²⁶, 5764804, F₇, 3, 4) (dual of [(5764804, 3), 17294386, 5]-NRT-code), using
- trace code [i] based on linear OOA(49¹³, 2882402, F₄₉, 3, 4) (dual of [(2882402, 3), 8647193, 5]-NRT-code), using
  - OA 2-folding and stacking [i] based on linear OA(49¹³, 5764804, F₄₉, 4) (dual of [5764804, 5764791, 5]-code), using
    - discarding factors / shortening the dual code based on linear OA(49¹³, 5764805, F₄₉, 4) (dual of [5764805, 5764792, 5]-code), using
      - constructionÂ X applied to C_e(3) âŠ‚ C_e(2) [i] based on
        linear OA(49¹³, 5764801, F₄₉, 4) (dual of [5764801, 5764788, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
        linear OA(49⁹, 5764801, F₄₉, 3) (dual of [5764801, 5764792, 4]-code or 5764801-cap in PG(8,49)), using an extension C_e(2) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [i]
        linear OA(49⁰, 4, F₄₉, 0) (dual of [4, 4, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(49⁰, s, F₄₉, 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(7⁷⁷, 3844378, F₇, 3, 9) (dual of [(3844378, 3), 11533057, 10]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(7¹¹, 1176, F₇, 3, 4) (dual of [(1176, 3), 3517, 5]-NRT-code), using
    - OA 2-folding and stacking [i] based on linear OA(7¹¹, 2352, F₇, 4) (dual of [2352, 2341, 5]-code), using
      - base reduction for projective spaces (embedding PG(5,49) in PG(10,7)) [i] based on linear OA(49⁶, 2352, F₄₉, 4) (dual of [2352, 2346, 5]-code), using
        1 times truncation [i] based on linear OA(49⁷, 2353, F₄₉, 5) (dual of [2353, 2346, 6]-code), using
        a code by Danev and Olsson [i]
  2. linear OOA(7⁶⁶, 3843202, F₇, 3, 9) (dual of [(3843202, 3), 11529540, 10]-NRT-code), using
    - trace code [i] based on linear OOA(49³³, 1921601, F₄₉, 3, 9) (dual of [(1921601, 3), 5764770, 10]-NRT-code), using
      - OOA 3-folding [i] based on linear OA(49³³, 5764803, F₄₉, 9) (dual of [5764803, 5764770, 10]-code), using
        discarding factors / shortening the dual code based on linear OA(49³³, 5764805, F₄₉, 9) (dual of [5764805, 5764772, 10]-code), using
        constructionÂ X applied to C_e(8) âŠ‚ C_e(7) [i] based on
        linear OA(49³³, 5764801, F₄₉, 9) (dual of [5764801, 5764768, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
        linear OA(49²⁹, 5764801, F₄₉, 8) (dual of [5764801, 5764772, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 5764800Â = 49⁴âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
        linear OA(49⁰, 4, F₄₉, 0) (dual of [4, 4, 1]-code) (see above)

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.