MinT - Information on Result #1201186

Information on Result #1201186

Digital (30, 42, 43731)-net over F₆₄, using net defined by OOA based on linear OOA(64⁴², 43731, F₆₄, 15, 12) (dual of [(43731, 15), 655923, 13]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(64⁴², 87463, F₆₄, 3, 12) (dual of [(87463, 3), 262347, 13]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(64⁷, 80, F₆₄, 3, 6) (dual of [(80, 3), 233, 7]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,233P) [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]
  2. linear OOA(64³⁵, 87383, F₆₄, 3, 12) (dual of [(87383, 3), 262114, 13]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(64³⁵, 262149, F₆₄, 12) (dual of [262149, 262114, 13]-code), using
      - discarding factors / shortening the dual code based on linear OA(64³⁵, 262151, F₆₄, 12) (dual of [262151, 262116, 13]-code), using
        constructionÂ X applied to C_e(11) âŠ‚ C_e(9) [i] based on
        linear OA(64³⁴, 262144, F₆₄, 12) (dual of [262144, 262110, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
        linear OA(64²⁸, 262144, F₆₄, 10) (dual of [262144, 262116, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
        linear OA(64¹, 7, F₆₄, 1) (dual of [7, 6, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(64¹, s, F₆₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.