“New bounds for n4(k,d) and classification of some optimal codes over GF(4)”


Върбанов, Златко (2004) “New bounds for n4(k,d) and classification of some optimal codes over GF(4)” Discrete Mathematics, Volume 281, Number 1-3, April 2004, pp.43-66, ISSN 0012-365X, https://www.scopus.com/record/display.uri?eid=2-s2.0-1842564007&origin=resultslist&sort=plf-f&src=s&sid=91c34d60728841d539afd57ab7fa5287&sot=autdocs&sdt=autdocs&sl=18&s=AU-ID%2856618122100%29&relpos=4&citeCnt=8&searchTerm=


 Let n4(k,d) be the minimum length of a linear [n,k,d] code over GF(4) for given values of k and d. For codes of dimension five, we compute the exact values of n4(5,d) for 75 previously open cases. Additionally, we show that n4(6,14)=24, n4(7,9)=18, and n4(7,10)=20. Moreover, we classify optimal quaternary codes for some values of n and k.
  Статия
 bound, linear code, classification


Природни науки, математика и информатика

Natural sciences, mathematics and informatics

 Издадено
  22154
 Златко Върбанов

10. H.Kanda, T.Maruta, "Nonexistence of some linear codes over the field of order four", Discrete Mathematics, Volume 341, Issue 10, October 2018, pp. 2676-2685; https://www.scopus.com/authid/detail.uri?authorId=56618122100

9. L.Lu, R.Li, L.Guo, "Entanglement-assisted quantum codes from quaternary codes of dimension five", International Journal of Quantum Information 15(3):1750017, March 2017, ISSN (print): 0219-7499; https://www.scopus.com/authid/detail.uri?authorId=56618122100

8. Lu, L., Li, R., Guo, L., "Maximal entanglement entanglement-assisted quantum codes constructed from linear codes", Quantum Information Processing, Volume 14, Issue 1, January 2015, Pages 165-182; https://www.scopus.com/authid/detail.uri?authorId=56618122100

7. Maruta, T., Tanaka, T., Kanda, H., "Some generalizations of extension theorems for linear codes over finite fields", Australasian Journal of Combinatorics 60(2), January 2014, pp.150-157; https://www.scopus.com/authid/detail.uri?authorId=56618122100

5. M.Ezerman, S.Ling, P.Sole, "Additive Asymmetric Quantum Codes", IEEE Transactions on Information Theory, Volume: 57, Issue: 8, Aug. 2011, pp. 5536 - 5550; https://www.scopus.com/authid/detail.uri?authorId=56618122100

6. R.Kanazawa, T.Maruta, "On Optimal Linear Codes over F8", The electronic journal of combinatorics 18(1), 2011, Paper #P34

4. N.Aydin, Ts.Asamov, "Search for good linear codes in the class of quasi-cyclic and related codes", World Scientific Review Volume, Series on Coding Theory and Cryptology, Selected Topics in Information and Coding Theory, pp. 239-285 (2010), ISBN 978-981-283-716-5

3. T.Maruta, M.Shinohara, A.Kikui, "On optimal linear codes over F5", Discrete Mathematics 309(6), April 2009, pp. 1255-1272; https://www.scopus.com/authid/detail.uri?authorId=56618122100

1. J.Zwanzger, "A Heuristic Algorithm for the Construction of Good Linear Codes", IEEE Transactions on Information Theory, Volume: 54 , Issue: 5 , May 2008, pp. 2388 - 2392; https://www.scopus.com/authid/detail.uri?authorId=56618122100

2. M.Takenaka, K.Okamoto, T.Maruta, "On optimal non-projective ternary linear codes", Discrete Mathematics, Volume 308, Issues 5–6, March 2008, pp. 842-854; https://www.scopus.com/authid/detail.uri?authorId=56618122100

Научният архив поддържа инициативата за отворен достъп OAI 2.0 с начален адрес: http://da.uni-vt.bg/oai2/