MinT - Information on Result #1540320

Information on Result #1540320

Linear OOA(4¹⁸⁷, 1924217, F₄, 3, 22) (dual of [(1924217, 3), 5772464, 23]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4¹⁸⁷, 1924217, F₄, 2, 22) (dual of [(1924217, 2), 3848247, 23]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4¹⁸⁷, 2097179, F₄, 2, 22) (dual of [(2097179, 2), 4194171, 23]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(4¹⁸⁵, 2097178, F₄, 2, 22) (dual of [(2097178, 2), 4194171, 23]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(4¹⁸⁵, 4194356, F₄, 22) (dual of [4194356, 4194171, 23]-code), using
    - constructionÂ X applied to C_e(21) âŠ‚ C_e(16) [i] based on
      1. linear OA(4¹⁷⁷, 4194304, F₄, 22) (dual of [4194304, 4194127, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 4¹¹âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
      2. linear OA(4¹³³, 4194304, F₄, 17) (dual of [4194304, 4194171, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 4¹¹âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
      3. linear OA(4⁸, 52, F₄, 4) (dual of [52, 44, 5]-code), using
        discarding factors / shortening the dual code based on linear OA(4⁸, 85, F₄, 4) (dual of [85, 77, 5]-code), using
        quaternary constacyclic codes with minimum distance 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(4¹⁸⁷, 481054, F₄, 27, 22) (dual of [(481054, 27), 12988271, 23]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row