MinT - Information on Result #2766798

Information on Result #2766798

Linear OOA(2²³⁸, 2099202, F₂, 4, 16) (dual of [(2099202, 4), 8396570, 17]-NRT-code), using strength reduction based on linear OOA(2²³⁸, 2099202, F₂, 4, 17) (dual of [(2099202, 4), 8396570, 18]-NRT-code), using

OOA 2-folding [i] based on linear OOA(2²³⁸, 4198404, F₂, 2, 17) (dual of [(4198404, 2), 8396570, 18]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁵³, 4103, F₂, 2, 8) (dual of [(4103, 2), 8153, 9]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(2⁵³, 8206, F₂, 8) (dual of [8206, 8153, 9]-code), using
      - 1 times truncation [i] based on linear OA(2⁵⁴, 8207, F₂, 9) (dual of [8207, 8153, 10]-code), using
        constructionÂ X4 applied to C_e(8) âŠ‚ C_e(6) [i] based on
        linear OA(2⁵³, 8192, F₂, 9) (dual of [8192, 8139, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
        linear OA(2⁴⁰, 8192, F₂, 7) (dual of [8192, 8152, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
        linear OA(2¹⁴, 15, F₂, 13) (dual of [15, 1, 14]-code), using
        strength reduction [i] based on linear OA(2¹⁴, 15, F₂, 14) (dual of [15, 1, 15]-code or 15-arc in PG(13,2)), using
        dual of repetition code with length 15 [i]
        linear OA(2¹, 15, F₂, 1) (dual of [15, 14, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
  2. linear OOA(2¹⁸⁵, 4194301, F₂, 2, 17) (dual of [(4194301, 2), 8388417, 18]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(2¹⁸⁵, 8388602, F₂, 17) (dual of [8388602, 8388417, 18]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹⁸⁵, large, F₂, 17) (dual of [large, large−185, 18]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [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.