SbEC‐DbED codes derived from experiments on a computer for semiconductor memory systems

Abstract

AbstractSingle byte (= b bits) error‐correcting and double byte error‐detecting (SbEC‐DbED) codes are useful for semiconductor memory systems with memory chips of b‐bit output per one address. In this paper, codes with information length k up to k = 128 bit for 2 b 8 are derived experimentally using a computer. As a result, codes with longer code lengths than before are obtained. In particular, as for the codes of b = 2 and k = 64, 12 check bits were required in the conventional codes, but the codes requiring only 10 check bits are derived by experiments and are an excellent result from a practical viewpoint too. In the derivation, each column in an H matrix of the code is regarded as an element in a Galois field GF (qr) where q = 2b (b is the number of bits in a byte) and r is the number of check bytes. to obtain codes with large code length, as many elements as possible are selected in GF(qr) satisfying the code condition. Here, a subset in a GF(qr) whose elements are linearly independent, is used to select the columns of the H matrix. Moreover, all the elements of GF(qr) arising as operation results in the derivation process can be in correspondence to the elements of the subset. Consequently, the objective sets are restricted and the derivation through computer experiments is facilitated.