New Minimum Distance Bounds for Linear Codes over GF(9)

Thirty-one new linear codes over GF(9) are constructed, and the nonexistence of thirty codes is proved.     

The nonexistence of some five-dimensional quaternary linear codes

Let n₄(k, d) be the smallest integer n, such that a quaternary linear [n, k, d; 4]-code exists. It is proved that n₄ (5, 20)=30, n₄(5, 42)⩾59, n₄(5, 45)⩾63, n₄(5, 64)⩾88, n₄(5, 80)=109, n₄(5, 140)⩾189, n₄(5, 143)⩾193, n₄ (5, 168)⩾226, n₄(5, 180)⩾242, n₄(5, 183)⩾246, n₄(5, 187)=251     

The Nonexistence of Ternary [284, 6, 188] Codes

Let [n, k, d] _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, 6, 188]₃ codes is proved, whence we get n ₃(6, 188) = 285 and n ₃(6, 189) = 286.     

New (n, r)-arcs in PG(2, 17), PG(2, 19), and PG(2, 23)

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 a new (95, 7)-arc, (183, 12)-arc, and (205, 13)-arc in PG(2, 17) are constructed, as well as a (243, 14)-arc and (264, 15)-arc in PG(2, 19). Likewise, good large (n, r)-arcs in PG(2, 23) are constructed and a table with bounds on m _r (2, 23) is presented. In this way many new 3-dimensional Griesmer codes are obtained. The results are obtained by nonexhaustive local computer search.     

A peptide-centric approach to breast cancer biomarker discovery utilizing label-free multiple reaction monitoring mass spectrometry

We report an approach for multiplex analysis of cancer biomarkers based on the measurement of diagnostic peptides in whole tissue protein digests. Label-free quantitation with MS3 multiple reaction monitoring (MRM) was developed to afford accurate analysis of prospective marker peptides in a panel of breast tumors. This approach provides an economical and robust alternative to stable isotope-based methods. It is equally applicable to the analysis of samples derived from tissue biopsy, aspirate, or plasma and can be easily translated to clinic.