---

 

Extended Quadratic Residue Codes over GF(2)

[8,4,4]	[48,24,12]	[98,49,16]	[152,76,20]
[18,9,6]	[72,36,12]	[104,52,20]	[168,84,24]
[24,12,8]	[74,37,14]	[114,57,16]	[192,96,28]
[32,16,8]	[80,40,16]	[128,64,20]	[194,97,28]
[42,21,10]	[90,45,18]	[138,69,22]	[200,100,32]

 

Quadratic Residue Codes over GF(2)

[7,4,3]	[47,24,11]	[97,49,15]	[151,76,19]
[17,9,5]	[71,36,11]	[103,52,19]	[167,84,23]
[23,12,7]	[73,37,13]	[113,57,15]	[191,96,27]
[31,16,7]	[79,40,15]	[127,64,19]	[193,97,27]
[41,21,9]	[89,45,17]	[137,69,21]	[199,100,31]

 

Quadratic Double Circulant Codes over GF(2)

[8,4,4]	[40,20,8]	[108,54,20]	[168,84,24]
[12,6,4]	[60,30,12]	[120,60,20]	[204,102,≤24]
[24,12,8]	[76,38,12]	[124,62,20]	[216,108,≤24]
[28,14,8]	[88,44,16]	[136,68,24]	[220,110,≤30]

 

---

References:

1. F. J. MacWilliams and N. J. A. Sloane, The Theory Error-Correcting Codes, North-Holland, 1977.

2. Philippe Gaborit, Carmen-Simona Nedeloaia and Alfred Wassermann, ''On the weight enumerators of duadic and quadratic residue codes'', IEEE Transactions on Information Theory, vol. 51, no.1, pp.402–407, January 2005.

3. J. Mykkeltveit, C. Lam and R. J. McEliece, ''On the weight enumerators of quadratic residue codes'', JPLTechnical Report 32-1526, vol.XII, pp.161–166, 1972.

4. C. Tjhai, M. Tomlinson, R. Horan, M. Ahmed  and M. Ambroze, ''On the efficient codewords counting algorithm and the weight distributions of the binary quadratic double circulant codes'', in Proc. IEEE Information Theory Workshop, Chengdu, China, 22–26 October 2006.

5. C. Tjhai, M. Tomlinson, R. Horan, M. Ahmed  and M. Ambroze, ''Some results on the weight distributions of the binary double circulant codes based on primes'', in Proc. 10th IEEE International Conference on Communication Systems, Singapore, 30 October–1 November 2006 (PDF preprint).

6. C. Tjhai, M. Tomlinson, M. Ambroze and M. Ahmed, ''On the weight distribution of the extended quadratic residue code of prime 137'', 7th International ITG Conference on Source and Channel Coding, Ulm, 14–16 January 2008. (PDF postprint)

---

Acknowledgements

We would like to thank the high performance computing resource provided by the PlymGRID team of the University of Plymouth.

---

Contact information

C. J. Tjhai (email: ctjhai@plymouth.ac.uk) or Martin Tomlinson (email: mtomlinson@plymouth.ac.uk)