MinT - Information on Result #1052057

Information on Result #1052057

Linear OOA(2²⁵⁸, 2162691, F₂, 4, 17) (dual of [(2162691, 4), 8650506, 18]-NRT-code), using OOA 2-folding based on linear OOA(2²⁵⁸, 4325382, F₂, 2, 17) (dual of [(4325382, 2), 8650506, 18]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁷³, 131081, F₂, 2, 8) (dual of [(131081, 2), 262089, 9]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(2⁷³, 262162, F₂, 8) (dual of [262162, 262089, 9]-code), using
    - discarding factors / shortening the dual code based on linear OA(2⁷³, 262163, F₂, 8) (dual of [262163, 262090, 9]-code), using
      - 1 times truncation [i] based on linear OA(2⁷⁴, 262164, F₂, 9) (dual of [262164, 262090, 10]-code), using
        constructionÂ X4 applied to C_e(8) âŠ‚ C_e(6) [i] based on
        linear OA(2⁷³, 262144, F₂, 9) (dual of [262144, 262071, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 2¹⁸âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
        linear OA(2⁵⁵, 262144, F₂, 7) (dual of [262144, 262089, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 2¹⁸âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
        linear OA(2¹⁹, 20, F₂, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,2)), using
        dual of repetition code with length 20 [i]
        linear OA(2¹, 20, F₂, 1) (dual of [20, 19, 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

The following results depend on this result:

	Result		Method
1	Linear OOA(2²⁵⁸, 2162691, F₂, 4, 16) (dual of [(2162691, 4), 8650506, 17]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2²⁵⁹, 2162691, F₂, 4, 17) (dual of [(2162691, 4), 8650505, 18]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²⁶⁰, 2162691, F₂, 4, 17) (dual of [(2162691, 4), 8650504, 18]-NRT-code)	[i]	OOA Duplication