“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.
 bound, linear code, classification

Природни науки, математика и информатика

Natural sciences, mathematics and informatics

 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

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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

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6. R.Kanazawa, T.Maruta, "On Optimal Linear Codes over F8", The electronic journal of combinatorics 18(1), 2011, Paper #P34; https://zbmath.org/?q=an%3A1221.94081

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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

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