New Results on Optimal (υ, 4, 1) Binary Cyclically Permutable Constant-Weight Codes

Мұқаба

Дәйексөз келтіру

Толық мәтін

Ашық рұқсат Ашық рұқсат
Рұқсат жабық Рұқсат берілді
Рұқсат жабық Тек жазылушылар үшін

Аннотация

Построены новые двоичные циклически перестановочные равновесные коды (ЦПР-коды) с параметрами (υ, 4, 1) для длин υ ⩽ 136, а также исправлено несколько табличных значений из работы авторов [1].

Авторлар туралы

T. Baicheva

Институт математики и информатики Болгарской академии наук

Email: tsonka@math.bas.bg
София, Болгария

S. Topalova

Институт математики и информатики Болгарской академии наук

Email: svetlana@math.bas.bg
София, Болгария

Әдебиет тізімі

  1. Байчева Ц., Топалова С. Классификация оптимальных двоичных циклически переста- новочных равновесных (v, 4, 1)-кодов и циклических 2-(v, 4, 1)-дизайнов для v ⩽ 76 // Пробл. передачи информ. 2011. V. 47. № 3. P. 10–18. https://www.mathnet.ru/rus/ppi2051
  2. Moreno O., Zhang Z., Kumar P.V., Zinoviev V.A. New Constructions of Optimal Cyclically Permutable Constant Weight Codes // IEEE Trans. Inform. Theory. 1995. V. 41. № 2. P. 448–455. https://doi.org/10.1109/18.370146
  3. Abel R.J.R., Buratti M. Difference Families // Handbook of Combinatorial Designs. Boca Raton: Chapman & Hall/CRC, 2007. Sec. VI.16. P. 392–410.
  4. Chung F.R.K., Salehi J.A., Wei V.K. Optical Orthogonal Codes: Design, Analysis, and Applications // IEEE Trans. Inform. Theory. 1989. V. 35. № 3. P. 595–604. https://doi.org/10.1109/18.30982
  5. Bird I.C.M., Keedwell A.D. Design and Applications of Optical Orthogonal Codes—A Sur- vey // Bull. Inst. Combin. Appl. 1994. V. 11. P. 21–44.
  6. Colbourn C.J., Dinitz J.H., Stinson D.R. Applications of Combinatorial Designs to Commu- nications, Cryptography, and Networking // Surveys in Combinatorics, 1999. Cambridge: Cambridge Univ. Press, 1999. P. 37–100.
  7. Nguyen Q.A., Gyo¨fri L., Massey J.L. Constructions of Binary Constant-Weight Cyclic Codes and Cyclically Permutable Codes // IEEE Trans. Inform. Theory. 1992. V. 38. № 3. P. 940–949. https://doi.org/10.1109/18.135636
  8. Bitan S., Etzion T. Constructions for Optimal Constant Weight Cyclically Permutable Codes and Difference Families // IEEE Trans. Inform. Theory. 1995. V. 41. № 1. P. 77–87. https://doi.org/10.1109/18.370117
  9. Fuji-Hara R., Miao Y. Optical Orthogonal Codes: Their Bounds and New Optimal Con- structions // IEEE Trans. Inform. Theory. 2000. V. 46. № 7. P. 2396–2406. https: //doi.org/10.1109/18.887852
  10. Baicheva T., Topalova S. Classification of Optimal (v, k, 1) Binary Cyclically Permutable Constant Weight Codes with k = 5, 6 and 7 and Small Lengths // Des. Codes Cryptogr. 2019. V. 87. № 2–3. P. 365–374. https://doi.org/10.1007/s10623-018-0534-x
  11. Brickell E.F., Wei V.K. Optical Orthogonal Codes and Cyclic Block Designs // Congr. Numer. 1987. V. 58. P. 175–182.
  12. Chen K., Zhu L. Existence of (q, k, 1) Difference Families with q a Prime Power and k = 4, 5 // J. Combin. Des. 1999. V. 7. № 1. P. 21–30. https://doi.org/10.1002/(SICI)1520-6610(1999)7:1<21::AID-JCD4>3.0.CO;2-Y
  13. Buratti M. Cyclic Designs with Block Size 4 and Related Optimal Optical Orthogonal Codes // Des. Codes Cryptogr. 2002. V. 26. № 1–3. P. 111–125. https://doi.org/10.1023/A:1016505309092
  14. Chang Y., Fuji-Hara R., Miao Y. Combinatorial Constructions of Optimal Optical Orthog- onal Codes with Weight 4 // IEEE Trans. Inform. Theory. 2003. V. 49. № 5. P. 1283–1292. https://doi.org/10.1109/TIT.2003.810628
  15. Abel R.J.R., Buratti M. Some Progress on (v, 4, 1) Difference Families and Optical Or- thogonal Codes // J. Combin. Theory Ser. A. 2004. V. 106. № 1. P. 59–75. https: //doi.org/10.1016/j.jcta.2004.01.003
  16. Buratti M., Pasotti A. Further Progress on Difference Families with Block Size 4 or 5 // Des. Codes Cryptogr. 2010. V. 56. № 1. P. 1–20. https://doi.org/10.1007/s10623-009-9335-6
  17. Wang X., Chang Y. Further Results on (v, 4, 1)-Perfect Difference Families // Discrete Math. 2010. V. 310. № 13-14. P. 1995–2006. https://doi.org/10.1016/j.disc.2010.03.017
  18. Reid C., Rosa A. Steiner Systems S(2, 4, v)—A Survey // Electron. J. Combin., Dynamic Survey DS18. 2010. https://doi.org/10.37236/39
  19. Colbourn M.J., Mathon R.A. On Cyclic Steiner 2-Designs // Ann. Discrete Math. 1980. V. 7. P. 215–253. https://doi.org/10.1016/S0167-5060(08)70182-1
  20. Hetman I. Steiner Systems S(2, 6, 121/126) Based on Difference Families, https://arxiv. org/abs/2401.08274 [math.CO], 2024.
  21. Baicheva T., Topalova S. Classification Results for (v, k, 1) Cyclic Difference Families with Small Parameters // Mathematics of Distances and Applications. Sofia: ITHEA, 2012. P. 24–30. Available at http://www.foibg.com/ibs_isc/ibs-25/ibs-25-p02.pdf.
  22. Baicheva T., Topalova S. An Update on Optimal (v, 4, 1) Binary Cyclically Permutable Constant Weight Codes and Cyclic 2-(v, 4, 1) Designs with Small v // Probl. Inf. Transm. 2024. V. 60. № 3. P. 189–198. https://doi.org/10.1134/S0032946024030037
  23. Colbourn C.J., Rosa A. Triple Systems, Oxford: Clarendon; New York: Oxford Univ. Press, 1999.
  24. P´alfy P. Isomorphism Problem for Relational Structures with a Cyclic Automorphism // Eu- ropean J. Combin. 1987. V. 8. № 1. P. 35–43. https://doi.org/10.1016/S0195-6698(87)80018-5

Қосымша файлдар

Қосымша файлдар
Әрекет
1. JATS XML
Жүктеу

© Russian Academy of Sciences, 2024