MinT - Information on Result #663241

Information on Result #663241

Linear OA(7¹¹⁰, 16825, F₇, 23) (dual of [16825, 16715, 24]-code), using (u,Â u+v)-construction based on

linear OA(7¹⁴, 18, F₇, 11) (dual of [18, 4, 12]-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OA(7¹, 3, F₇, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(7¹, s, F₇, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
  2. linear OA(7², 3, F₇, 2) (dual of [3, 1, 3]-code or 3-arc in PG(1,7)), using
    - dual of repetition code with length 3 [i]
  3. linear OA(7², 3, F₇, 2) (dual of [3, 1, 3]-code or 3-arc in PG(1,7)) (see above)
  4. linear OA(7³, 3, F₇, 3) (dual of [3, 0, 4]-code or 3-arc in PG(2,7) or 3-cap in PG(2,7)), using
    - complete OA / dual of code with only one code word [i]
  5. linear OA(7³, 3, F₇, 3) (dual of [3, 0, 4]-code or 3-arc in PG(2,7) or 3-cap in PG(2,7)) (see above)
  6. linear OA(7³, 3, F₇, 3) (dual of [3, 0, 4]-code or 3-arc in PG(2,7) or 3-cap in PG(2,7)) (see above)
linear OA(7⁹⁶, 16807, F₇, 23) (dual of [16807, 16711, 24]-code), using
- an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 16806Â = 7⁵âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]

Mode: Constructive and linear.

None.

None.