MinT - Information on Result #1364840

Information on Result #1364840

Linear OOA(4¹⁴², 524314, F₄, 2, 18) (dual of [(524314, 2), 1048486, 19]-NRT-code), using OOA 2-folding based on linear OA(4¹⁴², 1048628, F₄, 18) (dual of [1048628, 1048486, 19]-code), using

constructionÂ X with VarÅ¡amov bound [i] based on
1. linear OA(4¹³⁹, 1048624, F₄, 18) (dual of [1048624, 1048485, 19]-code), using
  - constructionÂ X applied to C_e(17) âŠ‚ C_e(12) [i] based on
    1. linear OA(4¹³¹, 1048576, F₄, 18) (dual of [1048576, 1048445, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
    2. linear OA(4⁹¹, 1048576, F₄, 13) (dual of [1048576, 1048485, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
    3. linear OA(4⁸, 48, F₄, 4) (dual of [48, 40, 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]
2. linear OA(4¹³⁹, 1048625, F₄, 15) (dual of [1048625, 1048486, 16]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 4¹³⁹Â > V_b^sâˆ’1(kâˆ’1)Â = 106 642560 461792 409923 627689 380487 584874 430228 575430 777377 059074 615722 713981 444427 [i]
3. linear OA(4², 3, F₄, 2) (dual of [3, 1, 3]-code or 3-arc in PG(1,4)), using
  - dual of repetition code with length 3 [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(4¹⁴², 524314, F₄, 3, 18) (dual of [(524314, 3), 1572800, 19]-NRT-code)	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Digital (124, 142, 524314)-net over F₄	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound