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 1-5 of 5 results.

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

A075936 Positions of check bits in code in A075934.

Original entry on oeis.org

31, 103, 171, 213, 301, 342, 439, 475, 494, 558, 595, 911, 1075, 1114, 1189, 1287, 1606, 1727, 1996, 2102, 2140, 2225, 2339, 2667, 2691, 3240, 3733, 4153, 4171, 4371, 4745, 4912, 5237, 5601, 5746, 6254, 6569, 6967, 7115, 7527, 8250, 8270
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, A075934, A075935, A075933, A075942.

A075939 Positions of check bits in code in A075937.

Original entry on oeis.org

63, 455, 729, 874, 948, 1259, 1393, 1437, 1660, 1678, 1831, 2002, 14343, 22553, 26666, 28724, 38955, 43057, 45085, 51260, 53262, 57383, 63506, 71873, 76098, 78212, 84547, 86683, 90923, 97268, 101446, 103596, 107829, 114136, 116281
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, A075937, A075938, A075942, A075933, A075945.

A075932 Basis for code in A075931.

Original entry on oeis.org

31, 227, 805, 1354, 6182, 10315, 18731, 35149, 67943, 393255, 655433, 1181959, 6291497, 10485837, 18874658, 35653635, 69337155, 136446255, 270666054, 1610612779, 2684354638, 4831838504, 9126807585, 17716871269, 34896740609
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, A075931, A075933, A075935, A075927, A075938.

Formula

a(n) = b(2^n), where b is A075931, the binary lexicode, d=5.
b(n) = XOR(a(i)) for all i where the i-th bit is set in n.

A075927 Basis for code in A075926.

Original entry on oeis.org

7, 25, 42, 75, 385, 642, 1155, 2184, 4233, 8330, 16523, 98305, 163842, 294915, 557064, 1081353, 2129930, 4227083, 8421504, 16810113, 33587330, 67141763, 134250632, 268468361, 536903818, 1073774731, 6442450945, 10737418242
Offset: 0

Views

Author

Bob Jenkins (bob_jenkins(AT)burtleburtle.net)

Keywords

Links

Crossrefs

Cf. A075928, A075929, A075930, A075926, A057716, A075933.

Formula

a(n) = b(2^n), where b is the Hamming code d=3.
b(n) = XOR(a(i)) where i is a bit set in n.
Showing 1-5 of 5 results.

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

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