—Two product array codes are used to construct the (24, 12, 8) binary Golay code through the direct sum operation. This construction provides a systematic way to find proper (8, 4, 4) linear block component codes for generating the Golay code, and it generates and extends previously existing methods that use a similar construction framework. The code constructed is simple to decode.

Landry, Minsky and Taylor (LMT) introduced two polynomial invariants of veering triangulations—the taut the polynomial. Here, we consider a pair polynomials associated to one triangulation, upper lower one, analogously polynomials. We prove that are equal. In contrast, same triangulation may differ by more than unit. give algorithms compute all these invariants. LMT related Teichmüller fibered ...

Ladder networks have been studied extensively using Fibonacci numbers, Chebyshev polynomials, Morgan-Voyce polynomials, Jacobsthal polynomials, etc. ([10], [11], [2], [14], [9]. [5], [3], and [4]). All these polynomials are, in fact, particular cases of the generalized polynomials defined by U„(x,y) = xU„_l(x,y)+yU„_2(x,y), (»>2) (la) with U0(x,y) = 0, Ul(x,y) = l, (lb) and V„(x, y) = xV^ix, y)...

The classical problem of counting the number real zeros a polynomial was solved long time ago by Sturm. analogous that has on unit circle is, however, still an open problem. In this paper, we show second can be reduced to first one through use suitable pair M\"obius transformations - often called Cayley have property mapping onto line and vice versa. Although method applies arbitrary complex po...

in this paper we demonstrate the existence of a set of polynomials pi , 1 i  n , which arepositive semi-definite on an interval [a , b] and satisfy, partially, the conditions of polynomials found in thelagrange interpolation process. in other words, if a  a1  an  b is a given finite sequence of realnumbers, then pi (a j )  ij (ij is the kronecker delta symbol ) ; moreover, the sum of ...

We introduce a reduction order called the weighted path order (WPO) that subsumes many existing reduction orders. WPO compares weights of terms as in the Knuth-Bendix order (KBO), while WPO allows weights to be computed by a wide class of interpretations. We investigate summations, polynomials and maximums for such interpretations. We show that KBO is a restricted case of WPO induced by summati...

Let K denote a field, and let V denote a vector space over K with finite positive dimension. We consider a pair of linear transformations A : V → V and A : V → V that satisfy the following two conditions: (i) There exists a basis for V with respect to which the matrix representing A is irreducible tridiagonal and the matrix representing A is diagonal. (ii) There exists a basis for V with respec...

Let K denote a field, and let V denote a vector space over K with finite positive dimension. We consider a pair of linear transformations A : V → V and A : V → V which satisfy the following two conditions: (i) There exists a basis for V with respect to which the matrix representing A is irreducible tridiagonal and the matrix representing A is diagonal. (ii) There exists a basis for V with respe...

The Assmus{Mattson theorem is a method to nd designs in linear codes over a nite eld. The purpose of this paper is to give an analogue of this theorem for Z 4 -codes by using the harmonic weight enumerator which is introduced by Bachoc. This theorem can nd some 5-designs in the lifted Golay code over Z 4 which were discovered previously by other methods. Index Terms { Z 4 -codes, Assmus{Mattson...