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Author Keri, Gerzson
Source CiteSeerX
Content type Text
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Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Dimensional Md Code ♦ Md Code ♦ Computational Result ♦ Dimensional Complete Md Code ♦ Regular Hyperovals ♦ Superregular Matrix ♦ General Theoretical Relation ♦ Dimensional Finite Projective Space ♦ Classical Arc ♦ Complete N-arc ♦ Main Conjecture
Abstract The number of (a) non-equivalent 2 and 3 dimensional MDS codes, (b) non-equivalent 3 dimensional complete MDS codes, (c) 3 dimensional MDS codes that can be described by classical arcs in PG(2, q), (d) arcs in regular hyperovals, and (e) 2 × n and 3 × n superregular matrices over GF(q) are established for q ≤ 19 and for a number of cases when 23 ≤ q ≤ 32. The equivalence classes over both PGL(k, q) and PΓL(k, q) are considered during the computations. Though, most of the results are reached by the help of a computer, also some general theoretical relations are formulated. A computational result of the paper is that there is no complete n-arc in PG(2, 31) for 23 ≤ n ≤ 30 and, consequently, the Main Conjecture for MDS Codes is true for arcs in up to 12 dimensional finite projective spaces of order 31, i.e., for MDS codes of up to 13 dimensions over GF(31).
Educational Role Student ♦ Teacher
Age Range above 22 year
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Education Level UG and PG ♦ Career/Technical Study