MinT - Information on Result #1475738

Information on Result #1475738

Linear OOA(8²³, 64527, F₈, 3, 5) (dual of [(64527, 3), 193558, 6]-NRT-code), using OOA stacking with additional row based on linear OOA(8²³, 64528, F₈, 2, 5) (dual of [(64528, 2), 129033, 6]-NRT-code), using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(8²³, 64528, F₈, 5) (dual of [64528, 64505, 6]-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OA(8⁰, 8066, F₈, 0) (dual of [8066, 8066, 1]-code), using
    - discarding factors / shortening the dual code based on linear OA(8⁰, s, F₈, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
      - OA with only one run / dual of code without redundancy [i]
  2. linear OA(8⁰, 8066, F₈, 0) (dual of [8066, 8066, 1]-code) (see above)
  3. linear OA(8⁰, 8066, F₈, 0) (dual of [8066, 8066, 1]-code) (see above)
  4. linear OA(8¹, 8066, F₈, 1) (dual of [8066, 8065, 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]
  5. linear OA(8¹, 8066, F₈, 1) (dual of [8066, 8065, 2]-code) (see above)
  6. linear OA(8¹, 8066, F₈, 1) (dual of [8066, 8065, 2]-code) (see above)
  7. linear OA(8⁶, 8066, F₈, 2) (dual of [8066, 8060, 3]-code), using
    - discarding factors / shortening the dual code based on linear OA(8⁶, 32768, F₈, 2) (dual of [32768, 32762, 3]-code), using
      - an extension C_e(1) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,1], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 2 [i]
  8. linear OA(8¹⁴, 8066, F₈, 5) (dual of [8066, 8052, 6]-code), using
    - trace code [i] based on linear OA(64⁷, 4033, F₆₄, 5) (dual of [4033, 4026, 6]-code), using
      - a code by Danev and Olsson [i]

Mode: 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.