MinT - Information on Result #1661724

Information on Result #1661724

Linear OOA(2⁶¹, 378, F₂, 6, 12) (dual of [(378, 6), 2207, 13]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2⁶¹, 378, F₂, 2, 12) (dual of [(378, 2), 695, 13]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2⁶¹, 517, F₂, 2, 12) (dual of [(517, 2), 973, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2⁶¹, 1034, F₂, 12) (dual of [1034, 973, 13]-code), using
  - 1 times truncation [i] based on linear OA(2⁶², 1035, F₂, 13) (dual of [1035, 973, 14]-code), using
    - constructionÂ X applied to C_e(12) âŠ‚ C_e(10) [i] based on
      1. linear OA(2⁶¹, 1024, F₂, 13) (dual of [1024, 963, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 2¹⁰âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      2. linear OA(2⁵¹, 1024, F₂, 11) (dual of [1024, 973, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 2¹⁰âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
      3. linear OA(2¹, 11, F₂, 1) (dual of [11, 10, 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]

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(2⁶¹, 377, F₂, 7, 12) (dual of [(377, 7), 2578, 13]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(2⁶¹, 377, F₂, 8, 12) (dual of [(377, 8), 2955, 13]-NRT-code)	[i]
3	Linear OOA(2⁶¹, 377, F₂, 18, 12) (dual of [(377, 18), 6725, 13]-NRT-code)	[i]