cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 60 results. Next

A075930 Positions of check bits in code in A075928.

Original entry on oeis.org

7, 11, 13, 14, 19, 21, 22, 25, 26, 28, 31, 35, 37, 38, 41, 42, 44, 47, 49, 50, 52, 55, 56, 59, 61, 62, 67, 69, 70, 73, 74, 76, 79, 81, 82, 84, 87, 88, 91, 93, 94, 97, 98, 100, 103, 104, 107, 109, 110, 112, 115, 117, 118, 121, 122
Offset: 0

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Author

Bob Jenkins (bob_jenkins(AT)burtleburtle.net)

Keywords

Comments

This sequence can be constructed from A057716 (all natural numbers other than the powers of two) by prepending an inverted parity bit.

Links

Crossrefs

Cf. A075928, A075929, A057716, A075936.

A075929 Basis for code in A075928.

Original entry on oeis.org

15, 51, 85, 150, 771, 1285, 2310, 4369, 8466, 16660, 33047, 196611, 327685, 589830, 1114129, 2162706, 4259860, 8454167, 16843009, 33620226, 67174660, 134283527, 268501264, 536936723, 1073807637, 2147549462, 12884901891
Offset: 0

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Author

Bob Jenkins (bob_jenkins(AT)burtleburtle.net)

Keywords

Links

A075926 List of codewords in binary lexicode with Hamming distance 3 written as decimal numbers.

Original entry on oeis.org

0, 7, 25, 30, 42, 45, 51, 52, 75, 76, 82, 85, 97, 102, 120, 127, 385, 390, 408, 415, 427, 428, 434, 437, 458, 461, 467, 468, 480, 487, 505, 510, 642, 645, 667, 668, 680, 687, 689, 694, 713, 718, 720, 727, 739, 740, 762, 765, 771, 772, 794, 797, 809
Offset: 0

Views

Author

Bob Jenkins (bob_jenkins(AT)burtleburtle.net)

Keywords

Comments

This is also the (infinite) d=3 Hamming code.

Links

Crossrefs

Cf. A075928, A075929, A075930, A075927, A057716, A075931.

A075931 List of codewords in binary lexicode with Hamming distance 5 written as decimal numbers.

Original entry on oeis.org

0, 31, 227, 252, 805, 826, 966, 985, 1354, 1365, 1449, 1462, 1647, 1648, 1676, 1683, 6182, 6201, 6341, 6362, 6915, 6940, 7136, 7167, 7532, 7539, 7567, 7568, 7753, 7766, 7850, 7861, 10315, 10324, 10408, 10423, 11118, 11121, 11149, 11154
Offset: 0

Views

Author

Bob Jenkins (bob_jenkins(AT)burtleburtle.net)

Keywords

Links

Crossrefs

Cf. A075928, A075929, A075930, A075932, A075933, A075924, A075926, A075937.

Programs

  • PARI
    a=vector(40); n=0; for (k=0, 11154, if (n==0 || vecmin(apply(o -> hammingweight(bitxor(k, o)), a[1..n]))>=5, print1 (a[n++]=k", "))) \\ Rémy Sigrist, Feb 09 2021

A075934 List of codewords in binary lexicode with Hamming distance 6 written as decimal numbers.

Original entry on oeis.org

0, 63, 455, 504, 1611, 1652, 1932, 1971, 2709, 2730, 2898, 2925, 3294, 3297, 3353, 3366, 12365, 12402, 12682, 12725, 13830, 13881, 14273, 14334, 15064, 15079, 15135, 15136, 15507, 15532, 15700, 15723, 20630, 20649, 20817, 20846, 22237
Offset: 0

Views

Author

Bob Jenkins (bob_jenkins(AT)burtleburtle.net)

Keywords

Links

Crossrefs

Cf. A075928, A075929, A075930, A075935, A075936, A075931, A075928, A075940.

A075937 List of codewords in binary lexicode with Hamming distance 7 written as decimal numbers.

Original entry on oeis.org

0, 127, 1927, 2040, 6553, 6630, 7710, 7777, 10922, 10965, 11565, 11602, 13107, 13132, 13492, 13515, 19252, 19275, 19635, 19660, 21165, 21202, 21802, 21845, 24990, 25057, 26137, 26214, 30727, 30840, 32640, 32767, 98731, 98772, 99884
Offset: 0

Views

Author

Bob Jenkins (bob_jenkins(AT)burtleburtle.net)

Keywords

References

  • J. H. Conway and N. J. A. Sloane, Lexicographic codes: error-correcting codes from game theory, IEEE Transactions on Information Theory, 32:337-348, 1986.

Links

Crossrefs

Cf. A075928, A075929, A075930, A075938, A075939, A075940, A075931, A075943.

Programs

  • C
    See Links section.

A075944 Basis for code in A075943.

Original entry on oeis.org

511, 15887, 116275, 412245, 693418, 3165290, 12603032, 21139155, 38803550, 201349286, 336626733, 609260174, 3221261509, 5374090380, 25769843817, 43016936625, 78384372260, 412317013686, 687266122367, 1238028666383
Offset: 0

Views

Author

Bob Jenkins (bob_jenkins(AT)burtleburtle.net)

Keywords

References

  • J. H. Conway and N. J. A. Sloane, Lexicographic codes: error-correcting codes from game theory, IEEE Transactions on Information Theory, 32:337-348, 1986.

Links

Crossrefs

Cf. A075928, A075929, A075930, A075943, A075945, A075947, A075938, A075950.

Formula

a(n) = b(2^n), where b is A075943, the binary lexicode, d=9.
b(n) = XOR(a(i)) for all i where the i-th bit is set in n.

A075945 Positions of check bits in code in A075943.

Original entry on oeis.org

255, 3855, 13107, 21845, 27306, 38506, 71576, 92115, 101470, 138406, 172589, 240014, 272069, 380556, 536169, 679601, 847140, 1072054, 1258879, 1397519, 2005450, 2121415, 2496892, 2738813, 3993667, 4241896, 4617503, 5821704
Offset: 0

Views

Author

Bob Jenkins (bob_jenkins(AT)burtleburtle.net)

Keywords

References

  • J. H. Conway and N. J. A. Sloane, Lexicographic codes: error-correcting codes from game theory, IEEE Transactions on Information Theory, 32:337-348, 1986.

Links

Crossrefs

Cf. A075928, A075929, A075930, A075943, A075944, A075948, A075939, A075951.

A075946 List of codewords in binary lexicode with Hamming distance 10 written as decimal numbers.

Original entry on oeis.org

0, 1023, 31775, 32736, 232551, 233368, 258168, 258951, 824491, 825172, 846004, 846667, 989388, 990003, 1008851, 1009452, 1386837, 1387178, 1398090, 1398453, 1484082, 1484493, 1497389, 1497810, 1687038, 1687041, 1688033
Offset: 0

Views

Author

Bob Jenkins (bob_jenkins(AT)burtleburtle.net)

Keywords

References

  • J. H. Conway and N. J. A. Sloane, Lexicographic codes: error-correcting codes from game theory, IEEE Transactions on Information Theory, 32:337-348, 1986.

Links

Crossrefs

Cf. A075928, A075929, A075930, A075947, A075948, A075943, A075940, A075952.

A075949 List of codewords in binary lexicode with Hamming distance 11 written as decimal numbers.

Original entry on oeis.org

0, 2047, 129055, 131040, 932067, 933660, 1032444, 1033987, 3299692, 3301011, 3383667, 3384972, 3957135, 3958384, 4037008, 4038255, 5548725, 5549386, 5591722, 5592405, 5935702, 5936553, 5990985, 5991862, 6747097, 6747174
Offset: 0

Views

Author

Bob Jenkins (bob_jenkins(AT)burtleburtle.net)

Keywords

References

  • J. H. Conway and N. J. A. Sloane, Lexicographic codes: error-correcting codes from game theory, IEEE Transactions on Information Theory, 32:337-348, 1986.

Links

Crossrefs

Cf. A075928, A075929, A075930, A075950, A075951, A075952, A075943, A075955.
Showing 1-10 of 60 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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