Remark on a result of Constantine

نویسنده

  • Padraig Ó Catháin
چکیده

In [1], Constantine proposed that a variant of the codes constructed in Theorem 1 might be a useful substitute for Hadamard matrices at orders where no Hadamard matrix is known to exist. His main result is a plug-in construction for codes of order 4q with 8q codewords and minimum distance 2q−2 using a Goethals-Seidel type array. He provides component matrices for odd prime powers q. Theorem 1 strengthens Constantine’s result in two ways. First, the orders at which his codes exist are a proper subset of the orders covered by Theorem 1. Second, at every order at which Constantine’s codes exist, we obtain an additional eight codewords without decreasing the minimum distance. It suffices to observe that there exist Hadamard matrices of order 4q+4 for all odd prime powers q. When q ≡ 3 mod 4, take the tensor product of a Paley type I matrix and a Hadamard matrix of order 4, while for q ≡ 1 mod 4, the tensor product of a Paley type II matrix with a Hadamard matrix of order 2 suffices. We also obtain existence results for many orders not covered by Constantine’s result, e.g. by applying Theorem 1 to Hadamard matrices coming from the Paley, twin-prime-power and Sylvester constructions.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A short remark on the result of Jozsef Sandor

It is pointed out that, one of the results in the recently published article, ’On the Iyengar-Madhava Rao-Nanjundiah inequality and it’s hyperbolic version’ [3] by J´ozsef S´andor is logically incorrect and new corrected result with it’s proof is presented.

متن کامل

A remark on Remainders of homogeneous spaces in some compactifications

‎We prove that a remainder $Y$ of a non-locally compact‎ ‎rectifiable space $X$ is locally a $p$-space if and only if‎ ‎either $X$ is a Lindel"{o}f $p$-space or $X$ is $sigma$-compact‎, ‎which improves two results by Arhangel'skii‎. ‎We also show that if a non-locally compact‎ ‎rectifiable space $X$ that is locally paracompact has a remainder $Y$ which has locally a $G_{delta}$-diagonal‎, ‎then...

متن کامل

Glazed Transitional Space as a Passive Heating System (Case Study: Glazed Loggias in Semi-Arid climate)

The environmental concern, ensuring comfort for occupants, pushed us to search for the impact of glazed loggia on thermal comfort of adjacent space in Cons tantine climate, having s trong climatic cons traints. An experimental s tudy is undertaken and described in this paper. Analysis of the in situ results is also discussed. This work shows that in winter glazed loggia benefit largely from sol...

متن کامل

A New Optimization Algorithm for Optimal Wind Turbine Location Problem in Constantine City Electric Distribution Network Based Active Power Loss Reduction

The wind turbine has grown out to be one of the most common Renewable Energy Sources (RES) around the world in recent years. This study was intended to position the Wind Turbine (WT) on a wind farm to achieve the highest performance possible in Electric Distribution Network (EDN). In this paper a new optimization algorithm namely Salp Swarm Algorithm (SSA) is applied to solve the problem of opt...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • CoRR

دوره abs/1511.08073  شماره 

صفحات  -

تاریخ انتشار 2015