Papers by Elena Metodieva
Some new ( n , r )-arcs in PG(2,31)
Electronic Notes in Discrete Mathematics, 2017
Improved lower bounds on m r (2,29)
Electronic Notes in Discrete Mathematics, 2017
A (k, r)-arc is a set of k points of a projective plane such that some r, but no r + 1 of them, a... more A (k, r)-arc is a set of k points of a projective plane such that some r, but no r + 1 of them, are collinear. The maximum size of a (k, r)-arc in P G(2, q) is denoted by mr(2, q). In this paper we established that m 3 (2, 17) ≥ 27, m 4 (2, 17) ≥ 41 and m 14 (2, 17) ≥ 221.
On the non-existence of [71, 55] linear codes over GF (5) 1
q codes be linear codes of length n, dimension k and minimum Hamming distance d over GF(q). Let d... more q codes be linear codes of length n, dimension k and minimum Hamming distance d over GF(q). Let d7(n, k) be the maximum possible minimum Hamming distance of a linear [n, k, d]7 code for given values of n and k. In this paper new lower and upper bounds for d7(n, k) are presented, when k ≤ 31 and 50 < n ≤ 100.
An (n, r)-arc is a set of n points of a projective plane such that some r, but no r + 1 of them, ... more An (n, r)-arc is a set of n points of a projective plane such that some r, but no r + 1 of them, are collinear. The maximum size of an (n, r)-arc in PG(2, q) is denoted by mr(2, q). In this paper we continue our research, started in [8], and present five new (n, r)-arcs with parameters (476, 18), (500, 19), (529, 20), (564, 21) and (592, 22). The constructed arcs improve the respective lower bounds on mr(2, q) in .
One of the main problems in coding theory is to construct codes with best possible minimum distan... more One of the main problems in coding theory is to construct codes with best possible minimum distances. In this paper good binary and ternary codes are presented, as well as one new code over GF(5).
An (n;r)-arc is a set of n points of a projective plane such that some r, but no r + 1 of them, a... more An (n;r)-arc is a set of n points of a projective plane such that some r, but no r + 1 of them, are collinear. The maximum size of an (n;r)-arc in PG(2;q) is denoted by mr(2;q). Using some good blocking sets in PG(2, 23) we establish that m22(2;23) 484, m21(2;23) 461, m20(2;23) 437, m19(2;23) 411, m18(2;23) 385 and m17(2;23) 360.
An (n, r)-arc is a set of n points of a projective plane such that some r, but no r + 1 of them, ... more An (n, r)-arc is a set of n points of a projective plane such that some r, but no r + 1 of them, are collinear. In this paper a (341, 15)-arc and a (388, 17)arc in PG(2,25) are constructed, as well as a (394, 16)-arc, a (501, 20)-arc and a (532, 21)-arc in PG(2,27).
An (n, r)-arc is a set of n points of a projective plane such that some r, but no r + 1 of them, ... more An (n, r)-arc is a set of n points of a projective plane such that some r, but no r + 1 of them, are collinear. The maximum size of an (n, r)-arc in PG(2, q) is denoted by mr(2, q). In this paper we establish that m11(2, 29) ≥ 258, m13(2, 29) ≥ 325, m14(2, 29) ≥ 361, m17(2, 29) ≥ 452 and m18(2, 29) ≥ 474. The presented results improve the respective lower bounds in .
Good (n;r)-arcs in PG(2, 23)
ABSTRACT An (n;r)-arc is a set of n points of a projective plane such that some r, but no r + 1 o... more ABSTRACT An (n;r)-arc is a set of n points of a projective plane such that some r, but no r + 1 of them, are collinear. The maximum size of an (n;r)-arc in PG(2, q) is denoted by m_r(2;q). In this paper we establish that m_3(2;23)\ge 35, m_4(2;23)\ge 58, m_5(2;23) \ge 77, m_6(2;23) \ge 97 and m_7(2;23) \ge 119.
q code be a linear code of length n, dimension k and Hamming minimum distance d over GF(q). In th... more q code be a linear code of length n, dimension k and Hamming minimum distance d over GF(q). In this paper record-breaking codes with parameters [30, 10, 15]5, [
An (n, r)-arc is a set of n points of a projective plane such that some r, but no r + 1 of them, ... more An (n, r)-arc is a set of n points of a projective plane such that some r, but no r + 1 of them, are collinear. In this paper new (95, 7)-arc and (205, 13)-arc in PG(2,17) are constructed, as well as (243, 14)-arc and (264, 15)-arc in PG(2,19).
Journal of Discrete Mathematics, 2013
An ( , )-arc is a set of n points of a projective plane such that some r, but no + 1 of them, are... more An ( , )-arc is a set of n points of a projective plane such that some r, but no + 1 of them, are collinear. The maximum size of an ( , )-arc in PG(2, q) is denoted by (2, q). In this paper, a new -arc in PG(2,19), a new (341, 15)-arc, and a (388, 17)-arc in PG(2,25) are constructed, as well as a (394, 16)-arc, a (501, 20)-arc, and a (532, 21)-arc in PG(2,27). Tables with lower and upper bounds on (2, 25) and (2, 27) are presented as well. The results are obtained by nonexhaustive local computer search.
An (n;r)-arc is a set of n points of a projective plane such that some r, but no r + 1 of them, a... more An (n;r)-arc is a set of n points of a projective plane such that some r, but no r + 1 of them, are collinear. The maximum size of an (n;r)-arc in PG(2;q) is denoted by mr(2;q). Using some good blocking sets in PG(2, 23) we establish that m22(2;23) 484, m21(2;23) 461, m20(2;23) 437, m19(2;23) 411, m18(2;23) 385 and m17(2;23)
Probl Inf Transm, 2004
q codes be linear codes of length n, dimension k, and minimum Hamming distance d over GF (q). Let... more q codes be linear codes of length n, dimension k, and minimum Hamming distance d over GF (q). Let n q (k, d) be the smallest value of n for which there exists an [n, k, d] q code. It is known from [1, 2] that 284 ≤ n 3 (6, 188) ≤ 285 and 285 ≤ n 3 (6, 189) ≤ 286. In this paper, the nonexistence of [284, 188] 3 codes is proved, whence we get n 3 (6, 188) = 285 and n 3 (6, 189) = 286.
An (n;r)-arc is a set of n points of a projective plane such that some r, but no r + 1 of them, a... more An (n;r)-arc is a set of n points of a projective plane such that some r, but no r + 1 of them, are collinear. The maximum size of an (n;r)-arc in PG(2, q) is denoted by mr(2;q). In this paper we establish that m3(2;23) 35, m4(2;23) 58, m5(2;23) 77, m6(2;23) 97 and m7(2;23) 119.
New ternary linear codes
IEEE Transactions on Information Theory, 1999
ABSTRACT
Discrete Mathematics, 2004
q -codes be linear codes of length n, dimension k and minimum Hamming distance d over GF (q). In ... more q -codes be linear codes of length n, dimension k and minimum Hamming distance d over GF (q). In this paper, the nonexistence of [105, 6, 68] 3 and [230, 6, 152] 3 codes is proved.
Discrete Mathematics, 2004
Let [n; k; d] q -codes be linear codes of length n, dimension k and minimum Hamming distance d ov... more Let [n; k; d] q -codes be linear codes of length n, dimension k and minimum Hamming distance d over GF(q). In this paper, 32 new codes over GF(5) are constructed and the nonexistence of 51 codes is proved.
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Papers by Elena Metodieva