MinT - Information on Result #1191064

Information on Result #1191064

Digital (44, 50, 5605921)-net over F₈, using net defined by OOA based on linear OOA(8⁵⁰, 5605921, F₈, 9, 6) (dual of [(5605921, 9), 50453239, 7]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(8⁵⁰, 5605922, F₈, 3, 6) (dual of [(5605922, 3), 16817716, 7]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(8⁸, 13520, F₈, 3, 3) (dual of [(13520, 3), 40552, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(8⁸, 13520, F₈, 2, 3) (dual of [(13520, 2), 27032, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(8⁸, 13520, F₈, 3) (dual of [13520, 13512, 4]-code or 13520-cap in PG(7,8)), using
        product of projective cap with cap in AG(4,Â 8) [i] based on linear OA(8⁴, 65, F₈, 3) (dual of [65, 61, 4]-code or 65-cap in PG(3,8)), using
        ovoid in PG(3,Â 8) [i]
  2. linear OOA(8⁴², 5592402, F₈, 3, 6) (dual of [(5592402, 3), 16777164, 7]-NRT-code), using
    - trace code [i] based on linear OOA(64²¹, 2796201, F₆₄, 3, 6) (dual of [(2796201, 3), 8388582, 7]-NRT-code), using
      - OOA 3-folding [i] based on linear OA(64²¹, large, F₆₄, 6) (dual of [large, large−21, 7]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [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.