MinT - Information on Result #1689951

Information on Result #1689951

Linear OOA(2²⁶⁰, 2503, F₂, 7, 38) (dual of [(2503, 7), 17261, 39]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²⁶⁰, 2503, F₂, 3, 38) (dual of [(2503, 3), 7249, 39]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²⁶⁰, 2747, F₂, 3, 38) (dual of [(2747, 3), 7981, 39]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2²⁶⁰, 8241, F₂, 38) (dual of [8241, 7981, 39]-code), using
  - discarding factors / shortening the dual code based on linear OA(2²⁶⁰, 8243, F₂, 38) (dual of [8243, 7983, 39]-code), using
    - constructionÂ X applied to C_e(38) âŠ‚ C_e(32) [i] based on
      1. linear OA(2²⁴⁸, 8192, F₂, 39) (dual of [8192, 7944, 40]-code), using an extension C_e(38) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,38], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 39 [i]
      2. 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]
      3. linear OA(2¹², 51, F₂, 4) (dual of [51, 39, 5]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹², 63, F₂, 4) (dual of [63, 51, 5]-code), using
        the primitive narrow-sense BCH-code C(I) with length 63Â = 2⁶âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [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(2²⁶⁰, 834, F₂, 49, 38) (dual of [(834, 49), 40606, 39]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row