MinT - Information on Result #1703989

Information on Result #1703989

Linear OOA(2²²³, 2201, F₂, 8, 33) (dual of [(2201, 8), 17385, 34]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²²³, 2201, F₂, 3, 33) (dual of [(2201, 3), 6380, 34]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²²³, 2748, F₂, 3, 33) (dual of [(2748, 3), 8021, 34]-NRT-code), using
- 2¹ times duplication [i] based on linear OOA(2²²², 2748, F₂, 3, 33) (dual of [(2748, 3), 8022, 34]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(2²²², 8244, F₂, 33) (dual of [8244, 8022, 34]-code), using
    - constructionÂ X applied to C_e(32) âŠ‚ C_e(26) [i] based on
      1. linear OA(2²⁰⁹, 8192, F₂, 33) (dual of [8192, 7983, 34]-code), using an extension C_e(32) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,32], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [i]
      2. linear OA(2¹⁷⁰, 8192, F₂, 27) (dual of [8192, 8022, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
      3. linear OA(2¹³, 52, F₂, 5) (dual of [52, 39, 6]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹³, 63, F₂, 5) (dual of [63, 50, 6]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 2⁶âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]

Mode: 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(2²²³, 1100, F₂, 40, 33) (dual of [(1100, 40), 43777, 34]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row