MinT - Information on Result #2699538

Information on Result #2699538

Linear OOA(8¹⁶⁵, 5592662, F₈, 3, 18) (dual of [(5592662, 3), 16777821, 19]-NRT-code), using 8¹ times duplication based on linear OOA(8¹⁶⁴, 5592662, F₈, 3, 18) (dual of [(5592662, 3), 16777822, 19]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(8²⁶, 260, F₈, 3, 9) (dual of [(260, 3), 754, 10]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(8⁸, 130, F₈, 3, 4) (dual of [(130, 3), 382, 5]-NRT-code), using
      - extracting embedded OOA [i] based on digital (4, 8, 130)-net over F₈, using
        trace code for nets [i] based on digital (0, 4, 65)-net over F₆₄, using
        net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
        the rational function field F₆₄(x) [i]
        Niederreiter sequence [i]
    2. linear OOA(8¹⁸, 130, F₈, 3, 9) (dual of [(130, 3), 372, 10]-NRT-code), using
      - extracting embedded OOA [i] based on digital (9, 18, 130)-net over F₈, using
        trace code for nets [i] based on digital (0, 9, 65)-net over F₆₄, using
        net from sequence [i] based on digital (0, 64)-sequence over F₆₄ (see above)
2. linear OOA(8¹³⁸, 5592402, F₈, 3, 18) (dual of [(5592402, 3), 16777068, 19]-NRT-code), using
  - trace code [i] based on linear OOA(64⁶⁹, 2796201, F₆₄, 3, 18) (dual of [(2796201, 3), 8388534, 19]-NRT-code), using
    - OOA 3-folding [i] 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.