MinT - Information on Result #809625

Information on Result #809625

Linear OOA(2²²⁶, 278, F₂, 2, 51) (dual of [(278, 2), 330, 52]-NRT-code), using OOA 2-folding based on linear OA(2²²⁶, 556, F₂, 51) (dual of [556, 330, 52]-code), using

discarding factors / shortening the dual code based on linear OA(2²²⁶, 557, F₂, 51) (dual of [557, 331, 52]-code), using
- constructionÂ X applied to C_e(50) âŠ‚ C_e(42) [i] based on
  1. linear OA(2²⁰⁸, 512, F₂, 51) (dual of [512, 304, 52]-code), using an extension C_e(50) of the primitive narrow-sense BCH-code C(I) with length 511Â = 2⁹âˆ’1, defining interval IÂ =Â [1,50], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 51 [i]
  2. linear OA(2¹⁸¹, 512, F₂, 43) (dual of [512, 331, 44]-code), using an extension C_e(42) of the primitive narrow-sense BCH-code C(I) with length 511Â = 2⁹âˆ’1, defining interval IÂ =Â [1,42], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 43 [i]
  3. linear OA(2¹⁸, 45, F₂, 7) (dual of [45, 27, 8]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹⁸, 48, F₂, 7) (dual of [48, 30, 8]-code), using
      - (u,Â u+v)-construction [i] based on
        linear OA(2⁶, 24, F₂, 3) (dual of [24, 18, 4]-code or 24-cap in PG(5,2)), using
        discarding factors / shortening the dual code based on linear OA(2⁶, 32, F₂, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
        Reedâ€“Muller code RM(1,5) [i]
        caps in base bÂ =Â 2 [i]
        linear OA(2¹², 24, F₂, 7) (dual of [24, 12, 8]-code), using
        extended Golay code G_e(2) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2²²⁶, 278, F₂, 2, 50) (dual of [(278, 2), 330, 51]-NRT-code)	[i]		Strength Reduction for OOAs