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 1-6 of 6 results.

A075928 List of codewords in binary lexicode with Hamming distance 4 written as decimal numbers.

Original entry on oeis.org

0, 15, 51, 60, 85, 90, 102, 105, 150, 153, 165, 170, 195, 204, 240, 255, 771, 780, 816, 831, 854, 857, 869, 874, 917, 922, 934, 937, 960, 975, 1011, 1020, 1285, 1290, 1334, 1337, 1360, 1375, 1379, 1388, 1427, 1436, 1440, 1455, 1478, 1481, 1525
Offset: 0

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Author

Bob Jenkins (bob_jenkins(AT)burtleburtle.net)

Keywords

Comments

The lexicode of Hamming distance d is constructed greedily by stepping through the binary vectors in lexicographic order and accepting a vector if it is at Hamming distance at least d from all already-chosen vectors.
The code is linear and infinite.
This is also the (infinite) d=4 Hamming code.
Lexicodes with even Hamming distance can be constructed from the preceding lexicode of odd Hamming distance by prepending a single parity bit.

Links

Crossrefs

Cf. A075929, A075930, A075926, A075934, A075944, A075945, A075946, A075937, A075949, etc.
A194851 is a subsequence.

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.

A075938 Basis for code in A075937.

Original entry on oeis.org

127, 1927, 6553, 10922, 19252, 98731, 164529, 295709, 559292, 1083662, 2132519, 4230034, 125829127, 427819033, 713031722, 1258291252, 6467616811, 10779361329, 19377684509, 36649828412, 71017955342
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, A075939, A075941, A075932, A075944.

Formula

a(n) = b(2^n), where b is A075937, the binary lexicode, d=7.
b(n) = XOR(a(i)) for all i where the i-th bit is set in n.

A075943 List of codewords in binary lexicode with Hamming distance 9 written as decimal numbers.

Original entry on oeis.org

0, 511, 15887, 16368, 116275, 116684, 129084, 129475, 412245, 412586, 423002, 423333, 494694, 495001, 504425, 504726, 693418, 693589, 699045, 699226, 742041, 742246, 748694, 748905, 843519, 843520, 844016, 844047, 858316
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, A075944, A075945, A075946, A075937, A075949.

A075947 Basis for code in A075946.

Original entry on oeis.org

1023, 31775, 232551, 824491, 1386837, 6330581, 25206065, 42278310, 77607100, 402698573, 673253467, 1218520349, 6442523019, 10748180761, 51539687634, 86033873250, 156768744521, 824634027372, 1374532244735, 2476057332766
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, A075946, A075948, A075944, A075941, A075953.

Formula

a(n) = b(2^n), where b is A075946, the binary lexicode, d=10.
b(n) = XOR(a(i)) for all i where the i-th bit is set in n.

A075950 Basis for code in A075949.

Original entry on oeis.org

2047, 129055, 932067, 3299692, 5548725, 25323961, 42250958, 202390343, 806394569, 1409681880, 2492481691, 12894763567, 21811487392, 103089080516, 176362268954, 824702327536, 1378954303613, 2508261212719
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, A075949, A075951, A075953, A075944, A075956.

Formula

a(n) = b(2^n), where b is A075949, the binary lexicode, d=11.
b(n) = XOR(a(i)) for all i where the i-th bit is set in n.
Showing 1-6 of 6 results.

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

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