The Packing Problem in Statistics, Coding Theory and Finite Projective Spaces: Update 2001

Hirschfeld, J. W. P.; Storme, Leo

doi:10.1007/978-1-4613-0283-4_13

Cited by 168 publications

(231 citation statements)

References 118 publications

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“…Tables with upper bounds on q up to 13 can be found in [1,8,12]. Tables for q = 17 can be found in [7,9,10].…”

Section: Resultsmentioning

confidence: 99%

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Construction of (n,r)-arcs in PG(2,q)

Braun¹,

Kohnert²,

Wassermann³

2005

Innov. Incidence Geom.

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“…Tables with upper bounds on q up to 13 can be found in [1,8,12]. Tables for q = 17 can be found in [7,9,10].…”

Section: Resultsmentioning

confidence: 99%

“…We define m r (2, q) as the maximum n such that an (n, r)-arc does exist. There are many results [1,12] concerning these numbers, and for q < 11 the exact values are known. In this paper we explicitly construct new arcs for 11 ≤ q ≤ 19 which contain more points than the previously known ones.…”

Section: Introductionmentioning

confidence: 99%

Construction of (n,r)-arcs in PG(2,q)

Braun¹,

Kohnert²,

Wassermann³

2005

Innov. Incidence Geom.

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“…However, the converse is not true (see Theorem 5.1 in Section V-C. Table X lists some known maximum value of n (see, e.g., [12], [28]) for the existence of [n, k] MDS linear codes over…”

Section: B Comparison With Bounds For Linear Mds Codesmentioning

confidence: 99%

On encoding symbol degrees of array BP-XOR codes

2015

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Abstract-Low density parity check (LDPC) codes, LT codes and digital fountain techniques have received significant attention from both academics and industry in the past few years. By employing the underlying ideas of efficient Belief Propagation (BP) decoding process (also called iterative message passing decoding process) on binary erasure channels (BEC) in LDPC codes, Wang has recently introduced the concept of array BP-XOR codes and showed the necessary and sufficient conditions for MDS [k + 2, k] and [n, 2] array BP-XOR codes. In this paper, we analyze the encoding symbol degree requirements for array BP-XOR codes and present new necessary conditions for array BP-XOR codes. These new necessary conditions are used as a guideline for constructing several array BP-XOR codes and for presenting a complete characterization (necessary and sufficient conditions) of degree two array BP-XOR codes and for designing new edge-colored graphs. Meanwhile, these new necessary conditions are used to show that the codes by Feng, Deng, Bao, and Shen in IEEE Transactions on Computers are incorrect.

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“…For q even, q ≥ 16, in PG(2, q), there exist irregular hyperovals, i.e., hyperovals which are not the union of a conic and its nucleus. We refer to [11] for the list of the known infinite classes of hyperovals in PG(2, q), q even.…”

Section: Introductionmentioning

confidence: 99%

A study of (x(q + 1), x; 2, q)-minihypers

Landjev

Storme

2009

Des. Codes Cryptogr.

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Abstract. In this paper, we study the weighted (x(q + 1), x; 2, q)-minihypers. These are weighted sets of x(q + 1) points in PG(2, q) intersecting every line in at least x points. We investigate the decomposability of these minihypers, and define a switching construction which associates to an (x(q + 1), x; 2, q)-minihyper, with x ≤ q 2 − q, not decomposable in the sum of another minihyper and a line, a (j(q + 1), j; 2, q)-minihyper, where j = q 2 − q − x, again not decomposable into the sum of another minihyper and a line. We also characterize particular (x(q + 1), x; 2, q)-minihypers, and give new examples. Additionally, we show that (x(q + 1), x; 2, q)-minihypers can be described as rational sums of lines. In this way, this work continues the research on (x(q + 1), x; 2, q)-minihypers by Hill and Ward [9], giving further results on these minihypers.

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The Packing Problem in Statistics, Coding Theory and Finite Projective Spaces: Update 2001

Cited by 168 publications

References 118 publications

Construction of (n,r)-arcs in PG(2,q)

Construction of (n,r)-arcs in PG(2,q)

On encoding symbol degrees of array BP-XOR codes

A study of (x(q + 1), x; 2, q)-minihypers

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