Partial covers of PG(n,q)

AbstractIn this paper, we show that a set of q+a hyperplanes, q>13, a≤(q−10)/4, that does not cover PG(n,q), does not cover at least qn−1−aqn−2 points, and show that this lower bound is sharp. If the number of non-covered points is at most qn−1, then we show that all non-covered points are contained in one hyperplane. Finally, using a recent result of Blokhuis, Brouwer and Szőnyi [8], we remark that the bound on a for which these results are valid can be improved to a<(q−2)/3 and that this upper bound on a is sharp

Binary and Ternary Quasi-perfect Codes with Small Dimensions

The aim of this work is a systematic investigation of the possible parameters of quasi-perfect (QP) binary and ternary linear codes of small dimensions and preparing a complete classification of all such codes. First we give a list of infinite families of QP codes which includes all binary, ternary and quaternary codes known to is. We continue further with a list of sporadic examples of binary and ternary QP codes. Later we present the results of our investigation where binary QP codes of dimensions up to 14 and ternary QP codes of dimensions up to 13 are classified.Comment: 4 page

Об одной гипотезе для форм с p-адическими коэффициентами

[Dodunekov Stefan; Dodunekov S.; Dodunekov Stefan M.; Додунеков Стефан]Russian. Bulgarian, English summar

t-good and t-proper linear error correcting codes

The probability of undetected error after using a linear code to correct errors is investigated. Sufficient conditions for a code to be t-good or t-proper for error correction are derived. Applications to various classes of codes are discussed

The MMD codes are proper for error detection

The undetected error probability of a linear code used to detect errors on asymmetric channel is afunction of the symbol error probability of the channeland involves the weight distribution of the code. The code is proper, if the undetected error probability increases monotonouslyin the symbol error probability. Proper codes are generally considered to perform well in error detection. We show in this paper that the Maximum MinimumDistance (MMD) codes are proper

t-good and t-proper linear error correcting codes

The probability of undetected error after using a linear code to correct errors is investigated. Sufficient conditions for a code to be t-good or t-proper for error correction are derived. Applications to various classes of codes are discussed

Error detection with a class of q-ary two-weight codes

We study a class of two-weight q-ary codes, considered by Baumert and McEliece, with regard to their properness or goodness in error detection. We prove for a large set of parameters that these codes are not good.For the remaining values of the parameters (which may or may notcorrespond to good codes) we determine if they are proper or no