MinT - Information on Result #903835

Information on Result #903835

Linear OOA(64⁸⁶, 4196350, F₆₄, 2, 18) (dual of [(4196350, 2), 8392614, 19]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(64¹⁷, 2049, F₆₄, 2, 9) (dual of [(2049, 2), 4081, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(64¹⁷, 4098, F₆₄, 9) (dual of [4098, 4081, 10]-code), using
  - constructionÂ X applied to C_e(8) âŠ‚ C_e(7) [i] based on
    1. linear OA(64¹⁷, 4096, F₆₄, 9) (dual of [4096, 4079, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
    2. linear OA(64¹⁵, 4096, F₆₄, 8) (dual of [4096, 4081, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 64²âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
    3. linear OA(64⁰, 2, F₆₄, 0) (dual of [2, 2, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(64⁰, s, F₆₄, 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(64⁶⁹, 4194301, F₆₄, 2, 18) (dual of [(4194301, 2), 8388533, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(64⁶⁹, 8388602, F₆₄, 18) (dual of [8388602, 8388533, 19]-code), using
  - discarding factors / shortening the dual code based on linear OA(64⁶⁹, large, F₆₄, 18) (dual of [large, large−69, 19]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [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.