MinT - Information on Result #1299022

Information on Result #1299022

Linear OA(3¹⁸⁷, 224, F₃, 87) (dual of [224, 37, 88]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(3¹⁸⁶, 222, F₃, 87) (dual of [222, 36, 88]-code), using
- constructionÂ X with VarÅ¡amov bound [i] based on
  1. linear OA(3¹⁸⁵, 220, F₃, 87) (dual of [220, 35, 88]-code), using
    - constructionÂ X with VarÅ¡amov bound [i] based on
      1. linear OA(3¹⁷⁷, 209, F₃, 87) (dual of [209, 32, 88]-code), using
        35 times truncation [i] based on linear OA(3²¹², 244, F₃, 122) (dual of [244, 32, 123]-code), using
        constructionÂ X applied to C_e(121) âŠ‚ C_e(120) [i] based on
        linear OA(3²¹², 243, F₃, 122) (dual of [243, 31, 123]-code), using an extension C_e(121) of the primitive narrow-sense BCH-code C(I) with length 242Â = 3⁵âˆ’1, defining interval IÂ =Â [1,121], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 122 [i]
        linear OA(3²¹¹, 243, F₃, 121) (dual of [243, 32, 122]-code), using an extension C_e(120) of the primitive narrow-sense BCH-code C(I) with length 242Â = 3⁵âˆ’1, defining interval IÂ =Â [1,120], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 121 [i]
        linear OA(3⁰, 1, F₃, 0) (dual of [1, 1, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]
      2. linear OA(3¹⁷⁷, 212, F₃, 82) (dual of [212, 35, 83]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3¹⁷⁷Â > V_b^sâˆ’1(kâˆ’1)Â = 2 076551 592417 161795 237968 439977 987255 823366 133971 125777 993064 114320 394722 656246 022363 [i]
      3. linear OA(3⁵, 8, F₃, 4) (dual of [8, 3, 5]-code), using
        discarding factors / shortening the dual code based on linear OA(3⁵, 11, F₃, 4) (dual of [11, 6, 5]-code), using
        Golay code G(3) [i]
  2. linear OA(3¹⁸⁵, 221, F₃, 86) (dual of [221, 36, 87]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3¹⁸⁵Â > V_b^sâˆ’1(kâˆ’1)Â = 16891 412246 536259 040630 456441 103759 611724 683014 169766 553778 874066 951905 156009 630490 494513 [i]
  3. linear OA(3⁰, 1, F₃, 0) (dual of [1, 1, 1]-code) (see above)
linear OA(3¹⁸⁶, 223, F₃, 86) (dual of [223, 37, 87]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 3¹⁸⁶Â > V_b^sâˆ’1(kâˆ’1)Â = 44195 239657 974543 741309 567702 199932 381878 327536 790152 572526 187229 498505 719977 812224 980921 [i]
linear OA(3⁰, 1, F₃, 0) (dual of [1, 1, 1]-code) (see above)

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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OA(3¹⁸⁸, 226, F₃, 87) (dual of [226, 38, 88]-code)	[i]		ConstructionÂ X with VarÅ¡amov Bound