MinT - Information on Result #900481

Information on Result #900481

Linear OOA(27⁵⁸, 4195707, F₂₇, 2, 10) (dual of [(4195707, 2), 8391356, 11]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(27¹², 1406, F₂₇, 2, 5) (dual of [(1406, 2), 2800, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(27¹², 2812, F₂₇, 5) (dual of [2812, 2800, 6]-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. linear OA(27¹, 703, F₂₇, 1) (dual of [703, 702, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(27¹, s, F₂₇, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
    2. linear OA(27¹, 703, F₂₇, 1) (dual of [703, 702, 2]-code) (see above)
    3. linear OA(27³, 703, F₂₇, 2) (dual of [703, 700, 3]-code), using
      - discarding factors / shortening the dual code based on linear OA(27³, 728, F₂₇, 2) (dual of [728, 725, 3]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 728Â = 27²âˆ’1, defining interval IÂ =Â [0,1], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [i]
    4. linear OA(27⁷, 703, F₂₇, 5) (dual of [703, 696, 6]-code), using
      - a code by Danev and Olsson [i]
linear OOA(27⁴⁶, 4194301, F₂₇, 2, 10) (dual of [(4194301, 2), 8388556, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(27⁴⁶, 8388602, F₂₇, 10) (dual of [8388602, 8388556, 11]-code), using
  - discarding factors / shortening the dual code based on linear OA(27⁴⁶, large, F₂₇, 10) (dual of [large, large−46, 11]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 27⁵âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [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.